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Recall that the product AB of two matrices A = (Aij)1

Recall that the product AB of two matrices A = (Aij)1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Discrete maths

Recall that the product AB of two matrices A = (Aij)1<i,j≤m and B = (Bij)1≤i,j≤m is a matrix C = AB such that Cij = Σk-1 Aik Bkj, for 1 ≤ i, j≤ m. Fortunately, these details are not relevant for this problem! Assume you have a procedure MaMu that, given two matrices, returns the product. Let M be some arbitrary square matrix. (a) Using procedure MaMu, describe (in pseudocode) a recursive algorithm that com- putes M2, n ≥ 1, and minimizes the total number of matrix multiplications made. (b) Analyze the number of times MaMu is called when computing M2" and give the related recurrence relation. Give a tight Big-O upper bound.
Transcribed Image Text:Recall that the product AB of two matrices A = (Aij)1<i,j≤m and B = (Bij)1≤i,j≤m is a matrix C = AB such that Cij = Σk-1 Aik Bkj, for 1 ≤ i, j≤ m. Fortunately, these details are not relevant for this problem! Assume you have a procedure MaMu that, given two matrices, returns the product. Let M be some arbitrary square matrix. (a) Using procedure MaMu, describe (in pseudocode) a recursive algorithm that com- putes M2, n ≥ 1, and minimizes the total number of matrix multiplications made. (b) Analyze the number of times MaMu is called when computing M2" and give the related recurrence relation. Give a tight Big-O upper bound.
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