Let A1 = 4 100 1 4 1 0 0 1 4 1 0 0 1 4 , I = 1000 0 100 0 0 1 0 000 1 , and O = 0000
Chapter 7, Problem 7.5.11(choose chapter or problem)
Let A1 = 4 100 1 4 1 0 0 1 4 1 0 0 1 4 , I = 1000 0 100 0 0 1 0 000 1 , and O = 0000 0000 0000 0000 . Form the 16 16 matrix A in partitioned form, A = A1 IO O I A1 I O O I A1 I O O I A1 . Let b = (1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6)t . a. Solve Ax = b using the conjugate gradient method with tolerance 0.05. b. Solve Ax = b using the preconditioned conjugate gradient method with C1 = D1/2 and tolerance 0.05. c. Is there any tolerance for which the methods of part (a) and part (b) require a different number of iterations?
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