= [BO 0 2.6 Suppose we have a 2n × 2n matrix A of the form A nonsingular matrices of size nx n. Suppose we want to solve

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Bo 0 2 6 Suppose We Have A 2n 2n Matrix A Of The Form A Nonsingular Matrices Of Size Nx N Suppose We Want To Solve 1 (107.25 KiB) Viewed 32 times

= [BO 0 2.6 Suppose we have a 2n × 2n matrix A of the form A nonsingular matrices of size nx n. Suppose we want to solve a system Ax where B and Care g - b. (a) What is the cost of computing an LU decomposition of A in the usual way? (b) What is the cost of computing LU decompositions of B and C? (c) Decompose b as b = [9. where c and d are vectors of length n. Explain how the system Ax = b can be solved using the LU decompositions of B and C di- rectly, while not computing the LU decomposition of A. Estimate the factor by which the computational cost is reduced compared to the situation where the LU decomposition of A is computed in the usual way.