(a) Find the spectral radius of the Jacobi and Gauss-Seidel iteration matrices when (b) Is A diagonally...

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(a) Find the spectral radius of the Jacobi and Gauss-Seidel iteration matrices when
(a) Find the spectral radius of the Jacobi and Gauss-Seidel

(b) Is A diagonally dominant?
(c) Use (10.86) to fix the optimal value of the SOR parameter. Verify that the spectral radius of the resulting iteration matrix agrees with the second formula in (10.86).
(d) For each iterative scheme, predict how many iterations are needed to solve the linear system A x = e1 to 4 decimal places, and then verify your predictions by direct computation.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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