1. Consider multiplication of two matrices A and B. each of size nxn. Let the product...
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1. Consider multiplication of two matrices A and B. each of size nxn. Let the product be matrix C = A x B. Suppose n = 2 for some integer k. Consider the classical matrix multiplication algorithm implemented using a divide-and-conquer approach. Each matrix is divided into 4 quadrants, each of size n/2xn/2. Then matrix multiplication is carried out as if all quadrants were single elements. C₁ CH [CC] - [AA] [BB (a) Write down the expression for each of the quadrants in the product matrix C. (The expression for C₁ is already provided.) C₁ = A x B₁+ A₁2 x B₂1 (b) Let T(n) be the total number of simple arithmetic operations (ie., number of mutiplica- tions and additions) for this divide-and-conquer algorithm to multiply two nxn matrices. Write a recurrence equation for T(n). Provide a brief explanation for each term. (e) Use Master-Theorem to obtain the solution. 1. Consider multiplication of two matrices A and B. each of size nxn. Let the product be matrix C = A x B. Suppose n = 2 for some integer k. Consider the classical matrix multiplication algorithm implemented using a divide-and-conquer approach. Each matrix is divided into 4 quadrants, each of size n/2xn/2. Then matrix multiplication is carried out as if all quadrants were single elements. C₁ CH [CC] - [AA] [BB (a) Write down the expression for each of the quadrants in the product matrix C. (The expression for C₁ is already provided.) C₁ = A x B₁+ A₁2 x B₂1 (b) Let T(n) be the total number of simple arithmetic operations (ie., number of mutiplica- tions and additions) for this divide-and-conquer algorithm to multiply two nxn matrices. Write a recurrence equation for T(n). Provide a brief explanation for each term. (e) Use Master-Theorem to obtain the solution.
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Related Book For
College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
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