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To solve systems like Ax = b where A is an invertible n x n matrix we write a program Solve(4, b) that takes a matrix A and right-hand side b as input and computes the solution to Ax = b. Suppose that the algorithm used by Solve(A, b) is the augmented matrix method. Let us say we need to solve k systems of the type Ax = b where the right-hand side changes, but the left hand side stays the same. We can do this by making k invocations to the procedure Solve(A, b). Can you come up with a better way of solving such systems, and characterize the improvement in operation count compared with making k calls to Solve(A, b)?

To solve systems like Ax = b where A is an invertible n x n matrix we write a program Solve(4, b) that takes a matrix A and right-hand side b as input and computes the solution to Ax = b. Suppose that the algorithm used by Solve(A, b) is the augmented matrix method. Let us say we need to solve k systems of the type Ax = b where the right-hand side changes, but the left hand side stays the same. We can do this by making k invocations to the procedure Solve(A, b). Can you come up with a better way of solving such systems, and characterize the improvement in operation count compared with making k calls to Solve(A, b)?

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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To solve systems like Ax = b where A is an invertible n x n matrix we write a program Solve(A, b) that takes a matrix A and right-hand side b as input and computes the solution to Ax = b. Suppose that the algorithm used by Solve(A, b) is the augmented matrix method. Let us say we need to solve k systems of the type Ax = b where the right-hand side changes, but the left hand side stays the same. We can do this by making & invocations to the procedure Solve(A, b). Can you come up with a better way of solving such systems, and characterize the improvement in operation count compared with making k calls to Solve(A, b)?
Transcribed Image Text:To solve systems like Ax = b where A is an invertible n x n matrix we write a program Solve(A, b) that takes a matrix A and right-hand side b as input and computes the solution to Ax = b. Suppose that the algorithm used by Solve(A, b) is the augmented matrix method. Let us say we need to solve k systems of the type Ax = b where the right-hand side changes, but the left hand side stays the same. We can do this by making & invocations to the procedure Solve(A, b). Can you come up with a better way of solving such systems, and characterize the improvement in operation count compared with making k calls to Solve(A, b)?
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