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