Consider solving the linear system Açx = b, where A An 2 1 0 1 2 1 012 B = = Ao + € B 0 1 1 −1 01 -1 -1 0 Use the residual correction method (6.111-6.113) to solve Ax = b for various values of €, with N = Ao. Give a condition of the form |≤| ≤ a, for some a, that will ensure convergence of the residual correction method.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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14. Consider solving the linear system Açx = b, where A
Ao
[
2 1
0
2
1
0 1 2
B
=
0
=
Ao + € B
1 1
-1
0
1
-1 -1 0
Use the residual correction method (6.111–6.113) to solve Ax b for various
values of €, with N = Ao. Give a condition of the form || ≤ a, for some a, that
will ensure convergence of the residual correction method.
Transcribed Image Text:14. Consider solving the linear system Açx = b, where A Ao [ 2 1 0 2 1 0 1 2 B = 0 = Ao + € B 1 1 -1 0 1 -1 -1 0 Use the residual correction method (6.111–6.113) to solve Ax b for various values of €, with N = Ao. Give a condition of the form || ≤ a, for some a, that will ensure convergence of the residual correction method.
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