Table 1 Approximate Cost for an n x n Matrix A with Large n Algorithm Cost in Flops Gauss-Jordan elimination (forward phase) Gauss-Jordan elimination (backward phase) n? LU-decomposition of A Forward...

Extracted text: Table 1 Approximate Cost for an n x n Matrix A with Large n Algorithm Cost in Flops Gauss-Jordan elimination (forward phase) Gauss-Jordan elimination (backward phase) n? LU-decomposition of A Forward substitution to solve Ly = b Backward substitution to solve Ux = y A-' by reducing [A |I] to [! | A-'] * 2n3 Compute A-'b * 2n 3


Extracted text: 4. The IBM Sequoia computer can operate at speeds in excess of 16 petaflops per second (1 petaflop = 1015 flops). Use Ta- ble 1 to estimate the time required to perform the following operations on an invertible 100,000 × 100,000 matrix A. (a) Execute the forward phase of Gauss-Jordan elimination. (b) Execute the backward phase of Gauss-Jordan elimina- tion. (c) LU-decomposition of A. (d) Find A-l by reducing [A | I] to [I | A¬'].