Walmart, Inc Essay Example | Topics and Well Written Essays - 500 words

Walmart, Inc - Essay Example Once inside, customers are able to easily change the app to store mode from online mode, thus creating room for them to enjoy interactive in-store experiences such as scanning bar codes for pricing and going through Wal-Mart’s interactive in-store circular, which will enable them to keep a record of everything theyve bought thus tracking overall expenditure. This new change adopted by the organization gives customers the ability to switch from online to store mode, giving Wal-Mart app users an opportunity to compare prices with other eTail sites and customers will now be able to purchase out-of-stock items online (Paul, Lori, & Hayagreeva, 2010). Wal-Mart was formed by Sam Walton. It was Sam’s leadership which brought about the rapid growth of Wal-Mart’s success. This colossal achievement was achieved as a result of Sam’s vision that he nurtured to realization by incorporating leadership and management practices that were highly effective. Wal-Mart’s current commitment to valuing people in the entire facet of its leadership, management and culture was cultivated overtime (Wollam, 2009). 3. How would you improve the change leadership process at this organization? Provide your suggestions and recommendations for improvement and explain why they will promote positive change within the organization. Come up with a comprehensive mission statement for the organization’s mission statement with its activities aligned with the organizations vision. For example, Wal-Mart’s primary goal is to offer and deliver high quality goods for all marketing, advertising and research, and development activities should be focused on the quality of goods, modes and speed of delivery. Task forces which bring together the organization’s leadership to discuss strategy should be created. This task force will be working together to come up with short- and long-term road maps for the organization which

History of Florence italy Essay Example | Topics and Well Written Essays - 750 words

History of Florence italy - Essay Example The popes encountered disagreements among themselves due to the difference in political alliances especially between the Italian and French popes who lived in Rome, and Avignon respectively. Any religious believer serving two popes, was intolerable and would be considered as a kin to being in hopeless/helpless passenger in an over speeding driverless automobile that would claim passenger’s life unsympathetically (Bonechi 43). The resolution to the pope issue was settled in a conference organized in 1409 which led to the appointment of a third pope, though the situation continued for a while till one pope settled on in 1417. The new pope led to resilience and creation of the papal state with the headquarters based in Italy. Due to the creation of a papal state all the tithes and funding directed to the church had to be channeled into one coffer, referred to as papal banker based in Florence (Bonechi 49). By the 15th Century Florence had already been famous and prosperous historically with fortunes in the banking industry and wool trades. However, the Black Death had wiped out the Italian population in the 14th century which resulted in bankruptcy of two banks. This led to occasional famine and civil unrest coupled with plague outbreak episodes and calamities which wobbled and shook Florence and its economy for a while (Bonechi 15). During the famine and economic strive, Florentines declined to be dominated by others, leading to repulsion of both Naples and Milan’s unwelcoming advancement. Due to the repulsion, Florence gained more power than it had during the pre- Plague forging ahead to secure Pisa as one of its port (this was a geographical item which Florence had not enjoyed previously) (Bonechi 38). During the third competition, the humanist believed that man was purportedly created in the image of God (Judea Christian) and given the ability to balance ideas in a meaningful manner.

The Personal Narratives Written By Beller And Thurber Essay Example for Free

The Personal Narratives Written By Beller And Thurber Essay Though the personal narratives written by Beller and Thurber were fairly short, they still revealed a lot about themselves, which essentially affected the experience of the reader. Through Thurber’s words, the reader gets a sense of who he was during his â€Å"University Days† by his many stories of the classes he claims he didn’t like. Beller on the other hand, reveals himself by his sense of style and description of the different unimportant articles of clothing. Both Beller and Thurber however use anecdotes to draw the reader in so there is a possibility of a connection,  thus altering the reader’s experience from what it would be like for them to just explain their point very dully. Right from the beginning of University Days, Thurber shares an amusing experience that grabs the readers attention immediately. Rather than just telling the reader his dislike for each class, he begins by saying â€Å"I passed all the other courses that I took at my university, but I could never pass botany. This was because all botany students had to spend several hours a week in a laboratory looking through a microscope at plant cells, and I could  never see through a microscope†(Thurber 26). From this, Thurber reveals his point of having some troubles with certain classes, but in a way where the reader finds it humorous and in a way where some readers might be able to relate. If Thurber were to just say he didn’t pass botany and economics and just left it at that, the reader wouldn’t be as engaged, nor would the reader actually understand what he had to go through.

Inverse Matrix Condition Number

Inverse Matrix Condition Number Inverse Matrix and Condition No. Saswati Rakshit Contents (Jump to) Aim Scope/Applications Introduction/Basics Objective System Flow Mathematics Figure/Descriptions Future Works References Aim: Consider 2 random matrices B and C of size 8Ãâ€"8 and write a cpgm / matlab to find A to satisfy the bellow condition: If AÃâ€"B = C Prove A = CÃâ€"B-1 And repeat the pgm for matrix of size 32Ãâ€"32 and 128Ãâ€"128. Scope/Application: In many applications we require inversion of matrix. In Linear Algebra, if AÃâ€"B=C, and from B and C we can compute A where A=CÃâ€"B-1. Stimulus-Response Computations In this framework, a system is provided with an input, called a  stimulus, and the resulting response of the system is measured. Some typical examples of stimuli are visual scenes i.e. if we increase incident light’s intensity then scene’s brightness will increase. The general goal is to find a  function  that accurately describes the relation between stimulus and response. Many systems can be modeled as a linear combination of equations, and thus written as a matrix equation: [Interactions]{response}= {stimuli} The system response can thus be found using the matrix inverse. Sometimes in image processing application if we have noisy image matrix and if we know what the noise matrix was added we can find the clear image by multiplying noisy image matrix with inverted noise matrix. Intro/Basics: We have considered two 8Ãâ€"8 matrices B and C. We suppose AÃâ€"B = C. Now by performing matrix multiplication on A and B we get C. Now we have to compute A from B and C. So AÃâ€"B = C and we have to proof A = CÃâ€"B-1. It is conceptually easy to compute AÃâ€"B = C and to find A = CB-1 for 2 dimensional matrices. But for large dimensional matrices it is not possible to easily compute because there is some round off errors in A which is the result of B-1 related to B’s condition number. Thecondition numberof a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. The condition number of a regular (square) matrix is the product of the norm of the matrix and the norm of its inverse and hence depends on the kind of matrix-norm. Condition number of a square nonsingular (invertible) matrix A is defined by: cond () = |||| ·|||| where the || ·|| above could be any of the norms defined for matrices. The numerical value of the condition number of an nÃâ€"n matrix depends on the particular norm used .The norm of a square matrix A is a non-negative real number denoted by ||A||. These matrix norms have the following properties: 1. ||A|| à ¯Ã¢â€š ¬Ã‚ ¾Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚ ° if A ≠  0 2. ||à ¯Ã‚ Ã‚ §A|| à ¯Ã¢â€š ¬Ã‚ ½Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ §Ãƒ ¯Ã‚ Ã‚ ¼Ã‚ ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| for any scalar value à ¯Ã‚ Ã‚ §Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ ³Ãƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| à ¯Ã¢â€š ¬Ã‚ «Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| à ¯Ã¢â€š ¬Ã‚ «Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ ´Ãƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼AB|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ µÃƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼Ax|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚  for any vector The norm of a matrix is a measure of how large its elements are. It is a way of determining the â€Å"size† of a matrix that is not necessarily related to how many rows or columns the matrix has. Three commonly used norms are: 1. The 1-norm: = This is the maximum absolute column sum where simply we sum the absolute values down each column and then take the biggest answer. 2. The inifinity-norm: = This is the maximum absolute row sum where simply we sum the absolute values along each row and then take the biggest answer. 3. The Euclidean norm: = This is the square root of the sum of all the squares. However, regardless of the norm, this condition number is always greater or equal to 1. If it is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy. If the condition number is large, then the matrix is said to be ill-conditioned. Practically, such a matrix is almost singular (not invertible), and the computation of its inverse or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has the condition number equal to infinity. Mathematically, if the condition number is less than ∞, the matrix is invertible. Numerically, there are roundoff errors which occur. A high condition number means that the matrix is almost non-invertible. The higher the condition number, the greater is the error in the calculation. This condition number helps to estimate how difficult a matrix will be to numerically invert. This condition number has certain properties: 1. For any matrix A, cond (A) ≠¥Ãƒ ¯Ã¢â€š ¬Ã‚  1 2. For identity matrix, cond (I) = 1 3. For any matrix A and scalar à ¯Ã‚ Ã‚ §, cond à ¯Ã¢â€š ¬Ã‚ ¨Ãƒ ¯Ã‚ Ã‚ §Ãƒ ¯Ã¢â€š ¬Ã‚  A) = cond (A) 4. For any diagonal matrix D = Diag(di), cond (D) = (max |di|)/(min|di|) A matrix A is ill-conditioned if relatively small changes in the input (in the matrix A) can cause large change in the output (the solution of Ax = b), i.e. the solution is not very accurate if input is rounded. Otherwise it is well-conditioned. If a matrix is ill-conditioned, then a small roundoff error can have a drastic effect on the output. However, if the matrix is well-conditioned, then the computerized solution is quite accurate. Thus the accuracy of the solution depends on the conditioning number of the matrix. Objective: To know how to determine the matrix inverse in an efficient manner. If AÃâ€"B=C and we have to prove A=CÃâ€"B-1 where A, B and C are nÃâ€"n matrices (n = 8, 32, 128) and find out the condition number of matrix using norms and finding accuracy. System flow: Steps performed: 1. Taking two matrices B and C of order 8Ãâ€"8. 2. Performing Matrix multiplication and result is stored in matrix A (performed using C Code) 3. Now calculate B-1 (performed using C Code) 4. Now again multiplying C and B-1. We get result matrix which is not accurate. 5. We need to calculate norms and condition number of a matrix (B) so we need to find norms of B and B-1. We can calculate norms in different way. Here we have used most popularly used 3 types of norms to calculate condition number of that matrix (B) which we need to get in inverse form. The norms are: 1-norm = Infinity-norm = iii) Euclidean norm = 6. Now we use norms to find condition number of matrix B by using formula cond (B) = |||| ·|||| Flow Diagram yes no Math For 22 Matrix First we consider a 22 matrix such that A= B= So by multiplying A and B we ge a 22 matrix C = Now We need to prove A=CB-1 So we need to find B-1 B-1 = 0.800 -0.200 -0.600 0.400 So now by doing CxB-1 = =A (proved) Before finding B-1 we can calculate condition number of B for the correctness of above proof, As we know cond (B) = |||| ·|||| Condition number using the 1-norm and inifinity-norm: Formula used Row Sum taking absolute values B = 2 13 3 47 Column sum 5 5 (taking absolute values) (max) Row sum B-1 = 0.800 -0.200 1.000 -0.600 0.400 1.000 Col Sum 1.4 .6 Applying 1-Norm = = maximum absolute column sum = 5, 1 = 1.4, So, cond1 (B) =  ·1 = 5Ãâ€"1.4= 7 Applying infinity-norm = = max absolute row sum = 7, ∞ = 1 So, cond∞ (B) =  ·Ã¢Ë†Å¾ = 7 Like this way we have also found condition number using the Euclidean norm which is = =5.47 = 1.095 CondE (B) =  ·E = 5.82 Here cond(B) is low in all cases.so we successfully get A =C. Because of low condition number of B,the inverse of B is acceptable. For 88 Matrix A = 1 2 3 4 1 2 2 1 2 3 1 4 3 4 2 1 4 1 3 2 3 3 1 2 2 2 1 4 2 2 2 1 3 2 1 4 3 1 2 1 1 1 2 3 1 2 2 1 1 2 1 2 1 2 1 2 2 2 3 3 2 1 2 2 B= 4 1 3 2 3 3 1 2 2 3 1 4 3 4 2 1 2 2 1 4 2 2 2 1 1 1 2 3 1 2 2 1 2 2 3 3 2 1 2 2 1 2 3 4 1 2 2 1 1 2 1 2 1 2 1 2 3 3 1 3 2 3 1 1 C=AÃâ€"B=27 30 28 52 27 37 28 20 35 38 42 64 35 46 35 27 42 35 41 59 37 43 31 27 29 29 32 49 28 37 27 22 34 30 35 50 32 39 28 25 22 24 24 41 21 29 22 17 23 25 22 39 22 30 20 15 34 33 30 53 32 40 28 23 B-1= -0.016 -0.429 0.063 0.524 0.063 -0.397 -0.222 0.587 -0.365 0.143 -0.540 0.048 0.460 -0.127 -0.111 0.508 0.095 0.071 -0.381 -0.143 0.119 0.381 -0.167 -0.024 0.270 -0.214 0.921 -0.905 -0.579 0.746 0.278 -0.484 0.206 0.571 0.175 -0.810 0.175 0.159 -0.111 -0.635 0.079 0.143 -0.317 0.381 -0.317 -0.016 0.111 0.063 -0.571 0.071 -0.714 1.857 0.786 -1.286 -0.500 0.643 0.159 -0.214 0.365 -0.238 -0.135 -0.032 0.722 -0.373 A=CÃâ€"B-1 =0.995 1.983 3.029 3.987 1.029 1.984 2.006 0.979 1.992 2.975 1.035 3.983 3.035 3.980 2.005 0.972 3.989 0.971 3.029 1.984 3.029 2.981 1.006 1.970 1.993 1.980 1.027 3.987 2.027 1.984 2.004 0.977 2.991 1.976 1.027 3.986 3.027 0.983 2.004 0.974 0.996 0.986 2.022 2.990 1.022 1.987 2.004 0.983 0.994 1.986 1.021 1.991 1.021 1.988 1.005 1.982 1.992 1.979 3.028 2.987 2.028 0.983 2.007 1.975 Relative Error for A11=(1-.995)=.005,A12= 0.017 and so on When we perform CÃâ€" B-1, we do not get original value of A because of B-1. If B-1 is not accurate we will not get accurate A. To get accuracy of A-1 we need to find condition number of B. As we know cond (B) = |||| ·|||| Condition number using the 1-norm and inifinity-norm: Formula used Row Sum taking absolute values B = 4 1 3 2 3 3 1 2 19 2 3 1 4 3 4 2 1 20 (max) 2 2 1 4 2 2 2 1 16 1 1 2 3 1 2 2 1 13 2 2 3 3 2 1 2 2 18 1 2 3 4 1 2 2 1 16 1 2 1 2 1 2 1 2 12 3 3 1 3 2 3 1 1 17 Column sum 16 16 15 25 16 19 13 11 (taking absolute values) (max) B-1 = For B-1, Row sum (max) taking absolute values = 6.428 (7th row) and column sum(max) taking absolute values = 4.906 (4th column) Applying 1-Norm = = maximum absolute column sum = 25, 1 = 4.906, So, cond1 (B) =  ·1 = 25Ãâ€"4.906 = 122.65 Applying infinity-norm = = max absolute row sum = 20, ∞ = 6.428 So, cond∞ (B) =  ·Ã¢Ë†Å¾ = 20Ãâ€"6.428 = 128.56. Like this way we have also found condition number using the Euclidean norm which is = 17.83. So here we can say that as the condition number of matrix B is high for all three cases, therefore the inverse of this matrix is showing numerical roundoff errors. Concept of Relative Error and Condition Number assume A is nonsingular and Ax = b if we change b to b + à ¢Ã‹â€ Ã¢â‚¬  b, the new solution is x + à ¢Ã‹â€ Ã¢â‚¬  x with A(x + à ¢Ã‹â€ Ã¢â‚¬  x) = b + à ¢Ã‹â€ Ã¢â‚¬  b the change in x is à ¢Ã‹â€ Ã¢â‚¬  x = A-1à ¢Ã‹â€ Ã¢â‚¬  b ‘condition’ of the solution †¢ the equations are well-conditioned if small à ¢Ã‹â€ Ã¢â‚¬  b results in small à ¢Ã‹â€ Ã¢â‚¬  x †¢ the equations are ill-conditioned if small à ¢Ã‹â€ Ã¢â‚¬  b can result in large à ¢Ã‹â€ Ã¢â‚¬  x [Singular matrix:A square matrix is called singular matrix if it’s determinant is zero.i.e. a singular matrix is not invertible] Example: Consider the linear system Ax = b with So = So here we easily find x= Now ,we change a small in b.let change in b is à ¢Ã‹â€ Ã¢â‚¬  b= So changed value= and solving the system A = we get =A= where x= changed to = due to small change in b. Now to calculate least condition number of the system we need to find Relative Error in the output and relative error in the input. Here we have relative error in the input/relative residual. = 0.01 Relative Error in the output =1 As we know, If condition number is closed to 1 then relative error and relative residual will be close. The condition number is defined by: Relative error in the output =Condition number Ãâ€" Relative error in the input. So,condition number= 1/.01=100 A matrix has high condition number is related to the fact that A is close to the singular matrix B= The following result shows that 1/cond(A) indicates how close A is to a singular matrix.Here cond(A) is 100 so, 1/cond(A)=.01 which is close enough. Description: The condition number associated with the  linear equation  Ax=bgives a bound on how inaccurate the solutionxwill be after approximation. This is before the effects of  round-off error  are taken into account; conditioning is a property of the matrix. Weshould think of the condition number as being the rate at which the solution,x, will change with respect to a change inb. Thus, if the condition number is large, even a small error inbmay cause a large error inx. On the other hand, if the condition number is small then the error inxwill not be much bigger than the error inb. The condition number may also be infinite, but this implies that the problem does not possess a unique, well-defined solution for each choice of data that is, the matrix is not invertible, and no algorithm can be expected to reliably find a solution. For large dimensional matrix such as for 3232 and 128128, the condition number is high and so inverse of that large dimensional matrix will give much error in output. Codes and Output Matrix multiplication int main() { int m, n, p, q, c, d, k, sum = 0; int A[10][10], B[10][10], C[10][10]; printf(Enter rows and columns of An); scanf(%d%d, m, n); printf(Enter the elements of An); for (c = 0; c for (d = 0; d scanf(%d, A[c][d]); printf(Enter rows and columns of Bn); scanf(%d%d, p, q); printf(Enter the elements of Bn); for (c = 0; c for (d = 0; d scanf(%d, B[c][d]); for (c = 0; c for (d = 0; d for (k = 0; k sum = sum + A[c][k]*B[k][d]; } C[c][d] = sum; sum = 0; } } for (c = 0; c for (d = 0; d printf(%dt, C[c][d]); printf(n); } getch(); } Matrix inverse #include #include int main() { float a[10][10],b[10][10],tem=0,temp=0,temp1=0,temp2=0,temp4=0,temp5=0; int n=0,m=0,i=0,j=0,p=0,q=0; printf(Enter size of 2d array(Square matrix) : ); scanf(%d,n); for(i=0;i { for(j=0;j { printf(Enter element no. %d %d :,i,j); scanf(%f,a[i][j]); if(i==j) b[i][j]=1; else b[i][j]=0; } } for(i=0;i { temp=a[i][i]; if(temp temp=temp*(-1); p=i; for(j=i+1;j { if(a[j][i] tem=a[j][i]*(-1); else tem=a[j][i]; if(temp temp=temp*(-1); if(tem>temp) { p=j; temp=a[j][i]; } } //row exchange in both the matrix for(j=0;j { temp1=a[i][j]; a[i][j]=a[p][j]; a[p][j]=temp1; temp2=b[i][j]; b[i][j]=b[p][j]; b[p][j]=temp2; } //dividing the row by a[i][i] temp4=a[i][i]; for(j=0;j { a[i][j]=(float)a[i][j]/temp4; b[i][j]=(float)b[i][j]/temp4; } //making other elements 0 in order to make the matrix a[][] an indentity matrix and obtaining a inverse b[][] matrix for(q=0;q { if(q==i) continue; temp5=a[q][i]; for(j=0;j { a[q][j]=a[q][j]-(temp5*a[i][j]); b[q][j]=b[q][j]-(temp5*b[i][j]); } } } printf(nnn); printf(Inverse of the matrix using Guass jordan elimination method:nn); for(i=0;i { for(j=0;j { printf(%.3f,b[i][j]); } printf(n); } getch(); } Matrix Condition Number #include #include int main() { int i,j,n,p,x=0,m=0,q,z=0,i1,j1; float Cond_A,poo,a[5][5],b[5],c[5],A[50][50],B[50][50],k[50],l[50]; printf(n n); printf(Program to find condition number of a matrix using infinity-norm); printf(n nn); printf(Enter rows and columns of An); scanf(%d%d, m, n); printf(Enter the elements of An); for (i = 0; i for (j = 0; j scanf(%f, A[i][j]); for(i=0;i { b[x]=0;c[x]=0; for(j=0;j { b[x]=b[x]+A[i][j]; } ++x; } for(i=0;i //FINDING LARGEST { if(b[i]>m) m=b[i]; } printf(largest row sum is %d,m); printf(nnEnter rows and columns of inv[A]n); scanf(%d%d, p, q); printf(Enter the elements of [A]n); for (i1 = 0; i1 for (j1 = 0; j1 scanf(%f, B[i1][j1]); for(i1=0;i1 { k[z]=0;l[z]=0; for(j1=0;j1 { k[z]=k[z]+B[i1][j1]; } ++z; } poo = k[0]; for(i1=1;i1 //FINDING LARGEST { if(k[i1]>poo) poo=k[i1]; } printf(largest row sum is %f,poo); Cond_A=m*poo; printf(nnCondition number of A is %f,Cond_A); //return 0; getch(); } Future works: If we work with a foggy image matrix(C) and we know the fog matrix(B) added to that image and the relation AÃâ€"B = C exist we will know whether it is possible to get the clear image matrix(A) by doing CÃâ€"B-1 calculating condition number of matrix B. If the condition number of matrix B is high then it is not possible to get accurate A from CÃâ€"B-1 as roundoff errors will increase. References: Matrix Inverse and Condition, Berlin Chen, Department of Computer Science Information Engineering, National Taiwan Normal University. Inversion error, condition number, and approximate inverses of uncertain matrices,  Laurent El Ghaoui, Department of Electrical Engineering and Computer Science,  University of California at Berkeley, Berkeley, CA 94720, USA. faculty.nps.edu/rgera/MA3042/2009/ch7.4.pdf www.rejonesconsulting.com/CS210_lect07.pdf http://teal.gmu.edu/ececourses/ece699/notes/note4.html Weisstein, Eric W. Matrix Norm. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/MatrixNorm.html

A Comparison between To His Coy Mistress and Sonnet 116 Essays -- Andr

A Comparison between To His Coy Mistress and Sonnet 116 The poem "To His Coy Mistress" was written in the mid 17th century by Andrew Marvell, being written in this time Marvell's poem was unable to be published as its taboo content was unfavoured by the puritans in power at the time. Whereas "Sonnet 116" by William Shakespeare was written in the late 16th century, a time of liberation and freedom for the stage and literature. Both poems are similar in theme and yet different in approach, they both pursue the theme of love although Marvell in a satirical Carpe Diem love style whereas Shakespeare in a traditional sonnet style. "To His Coy Mistress" by Andrew Marvell is about a young mans attempts to lure a woman into bed the true theme of the poem being more lust than love, the poem is in fact a parody of Carpe Diem love poetry and critiques the approach of an over eager young lover. "Sonnet 116" takes a more serious approach to the theme of love addressing the concept of eternal love "love alters not with his brief hours and weeks, But bears it out even to the edge of doom". The voice of the two poems also changes dramatically with Marvell there is an eager young lover willing to change tactics often in order achieve his goal. The voice is fickle and immature it evokes little sympathy from the reader and has rather a comic tone to it, this comic tone is highlighted by the fact that the poem is written in an iambic rhythm with four heavy stresses generally a rhythm used for comic value as it short and snappy allowing just the right amount of time for punnery and wit this effect is backed up by the poems rhyming couplets generally a rhythm used for comic value as it has a light tone to it. Shakes... ...imself merely a victim in a constant struggle to keep righteousness alive and if winning is impossible then better to lose a lot than a little "Thus, though we cannot make our Sun Stand still, yet we will make him run.". Shakespeare also ends on a rhyming couplet though this modest couplet is to lighten the serious tone "If this be error and upon me proved, I never writ, nor no man ever loved." though Shakespeare stresses that unless love is timeless and priceless and infallible it is nonexistent for Shakespeare believes there are no half measures in love. I personally enjoyed both poems though I preferred William Shakespeare's "Sonnet 116" as I feel the more serious classic approach to love makes more enjoyable reading, although the comic approach of Andrew Marvell's "To His Coy Mistress" was entertaining it did become quite tedious after a while.

The marketing of the Bridge Cafe Buffets is aimed towards all age groups. :: Business and Management Studies

The marketing of the Bridge Cafe Buffets is aimed towards all age groups. As the Bridge is part of the church buffets are offered for weddings INTRODUCTION This report was commissioned by Mrs A Bernard to show my understanding of the tools, techniques and ideas presented in the marketing module. The report will cover marketing orientation, practice approach, impact and buyer behaviour. Development of marketing segments and the marketing mix. To display my understanding I have used the Bridge Cafà ©, which has been trading for eighteen months and is expanding its services. It is part of the Christ Church community outreach program and is designed to offer good food at a very reasonable price. The marketing of the Bridge Cafe Buffets is aimed towards all age groups. As the Bridge is part of the church buffets are offered for weddings, birthdays, christenings, blessings and funerals as well as family functions and also as part of the conference facilities. With such a wide age range of customers the marketing has to appeal to a huge range of people from a variation of backgrounds. The service the Bridge offers can be tailor made to fit to the client’s needs and taste as well as a pre defined menu of various prices. With the ability to meet with clients for a more personal touch or by telephone, fax or e-mail for a faster more efficient service we can stay ahead in research and the development as trends change and different age groups have different tastes. We know our customers as we all eat and have an understanding of different diets and customs relating to religion. The clients that have already used the Bridge Buffets Service have found it easier to approach them to arrange a tailor designed menu for their guests as the staff are very approachable and are willing to spend time talking to the clients and their needs and desires. With this type of relationship with the client it is hoped that they will use the service again. The buffet service prides itself on producing home made and home baked products fresh to the client, which is catered to all sized buffets. Buffets can be organised at short notice (twenty four hours) and still uphold the same home made traditions. The marketing in practice fits in with the definition â€Å"Marketing is the management process which identifies, anticipates and supplies customer requirements efficiently and profitably† (The Chartered Institute of Marketing) as the client is in contact with a senior member of the team who knows and understand both the client needs and the practical aspect of the catering team.

5 Hour Energy Marketing Analysis

Dissecting A Marketing Strategy: 5 Hour Energy As he returned from a natural products trade show, Manoj Bhargava wondered to himself, â€Å"If I’m tired, do I also have to be thirsty? † As he contemplated this realization, he began to process it as a comparison of treatment of both a stomachache and a headache. Six months later he was entering one of the most saturated markets in the country, with a revolutionary product and a marketing plan that evolved from the placeholder name it still bears on the 3. 5 million units sold each year. -Hour Energy grossed north of $600 million last year and currently holds a 90% market share in the energy-shot business. Much of the company’s success can be attributed to a stringent customer-focused marketing plan, intent on distinguishing themselves in a competitive market by sharply reacting to customer focus groups. In dissecting the marketing strategy of Living Essential LLC’s 5-Hour Energy, I will detail how the compa ny was able to successfully target a market and position its’ product for sustained, long-run profitability. Market segmentation† is described as dividing a market into distinct segments that have similar needs or behaviors and behave in similar ways. Living Essential’s Bhargava had a product he believed could compete in the rapidly expanding energy drink market. The focus now shifted to identifying target groups of individuals that could be pulled away from the major players, such as Red Bull and Monster. With a goal to ambush the energy drink market with a customer-responsive product, Living Essential began laying out a $60 million research plan to identify a target market and develop a solid positioning strategy.The team of statisticians and psychologists embarked on a 36 month, nationwide research quest, utilizing focus groups, behavioral data collection, survey research and cross-sectional market analysis. At the core of this effort was a belief that in a mo nopolistically competitive market, the product needed to differentiate itself by directly fulfilling customer demands. The most glaring result of the company’s massive marketing research was that creating a profitable position in the energy drink market was only going to be possible by differentiating 5-Hour Energy from much larger conglomerate distributers.The product, in and of itself, possessed a points of parity laundry list when compared to other energy promoting soft drinks. Research showed that consumers were virtually indifferent as to the flavor, content and end-results of popular brands. The data did, however, produce several key areas where the potential for product differentiation shown out like a beacon of light in a cavernous black hole. Living Essential’s marketing team began swiftly developing a plan based on these very points of differentiation, which would slingshot the company into the market leader in only three short months.Equipped with the knowle dge about the target market they wanted to reach and the competitive advantage opportunities within the market, Living Essential began to refine its’ product. The marketing research results were at the forefront of product development. The decision was made that the company would not compete in refrigerated coolers with larger producers. One of the many customer complaints about energy drinks is that they need to consume nearly 12 ounces of a highly caffeinated, sugary beverage in order to get the jolt for which they were looking.From this data, 5-Hour Energy’s most important product concept was born: two-ounce bottles. Living Essential founder Manaj Bhargava had unknowingly identified one of the products biggest points of differentiation nearly a year prior on his return flight from the natural products conference: Must you be thirsty, because you’re tired? The answer from product focus groups was a resounding: â€Å"No! † Purchasers of energy drinks sim ply wanted energy. They were not engrossed in the requisite consumption of needless sugar calories that would, ultimately, lead to a â€Å"crash†, once the body had expended the artificial energy.The 5-Hour Energy product was now developing, in an effort to fulfill customer demand. This was the first major evolution toward becoming a demand-marketed product. Simple observation of the advertising efforts of popular energy drinks will lead you to the target demographic that energy drink producers hope their product will attract. If you have ever seen ESPN’s extreme sports competition, the X Games, the percentage odds are that you are a 13-17 year old boy.Even if you don’t happen to fall into that category, it would be glaringly obvious that energy drinks have deemed this demographic as their primary consumer targets. Nearly every competitor’s outerwear is littered with red-winged patches and most are promptly provided with a post-competition energy drink, l ogo facing outwards, at the conclusion of their â€Å"extreme† event. 5-Hour Energy’s marketing team consequently posed the question following their research results: â€Å"Are teens the only people in this world who are looking for extra energy? After all, it might be said that young boys have plenty of energy without caffeinated encouragement. Living Essential now had its’ second major point of differentiation on which to launch a marketing campaign. Seeking a niche that would give access to the energy drink market, Living Essential positioned itself as a product focused on individuals who work long hours, maintain non-traditional schedules and hold alertness-critical positions. Contrary to their competition, 5-Hour Energy attempted to appeal to demographics such as stay-at-home moms, doctors and professional athletes.Advertising efforts were geared toward weary professionals in contrast to BMX riding thrill-seekers. The underlying theory was that everyone ne eds energy. That being said, there was no room in the market for yet another energy drink. Living Essential could not bring forth another comparable product and compete with the brand recognition Red Bull and Monster already had in place. Using research data, Living Essential had identified the product’s differentiation advantages and the target market for optimizing sustained profitability in the energy drink market.The company, still directionally led by market research, now needed to determine at what price consumers would value their product. The conclusion that 5-Hour Energy could not effectively compete with large manufacturers was made, due mostly to the cost of retail space in refrigerated coolers. By making this concession however, it forced the upstart manufacturers to explore the retail spaces and the implicit nature of the product actually created a competitive advantage. The answer lay in the physical size of the product. Because 5-Hour Energy was not marketing i tself as an energy â€Å"beverage,† it didn’t eed to place the product in coolers next to Pepsi and Coca-Cola. Instead, the company made the decision to market 5-Hour Energy as a point-of-sale item. There was no need to have the bottles chilled, as consumers placed no additional value in temperature of only 2 ounces of consumable liquid. Next, they determined the size of the product gave them a pricing advantage as well. The cost of production for a 2-ounce product, as compared to the average 8-12 ounces of the competitors’ energy drinks, was far more cost effective.By reducing profit margins slightly, in order to sell 5-Hour Energy at a lower cost to consumer, they were able to increase the product’s value compared to competition. Living Essentials introduced the product in test markets at GNC stores in several geographic markets priced at two bottles for $5. After one week, the health food store reported that some of its stores had actually implemented wait-lists for the next shipments of 5-Hour Energy. The team at Living Essential realized they had a unique product, untapped target market and price point, that had endless potential.Bound still by the inability to financially support a large mainstream distribution, the company hired small distributors to peddle the product to convenience stores, encouraging them to put it on the counter next to lighters and key chains. It did not take long for larger competitors to take notice of the success that 5-Hour Energy was enjoying. The tiny, upstart package had not only stolen market share from the big names in the energy drink market, it had created from this share an entirely different market. The term Energy Shot was born.Today, all the major manufacturers of energy drinks have scrambled to enter the energy shot market, but 5-Hour Energy has the only real brand-recognition. Living Essential spends a modest amount on advertising in order to maintain its’ leadership position, but continues with a no-frills approach. Like the name of the product, which was only meant as a place holder originally until a marketable name was conceived, 5-Hour Energy delivers an old fashioned Proctor & Gamble message: Here’s the product, Here’s the features; Here’s the Benefits.It has been said, that one does not need to have invented rubber to sell tires. 5-Hour Energy did not create a market in energy promoting beverages. In fact, their recognition that they could not have survived in such a market, is the primary reason for their success. The progression of Living Essentials energy shot product reinforces the principles of marketing and the forces that good marketing can have on consumer behaviors. When the focus shifts from selling people your product, to producing the product they want, the odds of sustained profitability are exponentially increased. -Hour Energy utilized fundamentally sound research techniques to develop a marketing plan that emphasiz ed the competitive advantage of the product. With continued attention to the static nature of their target market and demographic segmentations, the company can look forward to a long and prosperous future. After all, people will always be thirsty, and they will always be tired, however, both problems do not need to be remedied with one product.