| 1 |
One can change A and b by preconditioning
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| 2 |
M1-1 A (M2-1 M2)x = M1-1 b
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| 3 |
is same equation as before for any choice of matrices M1 and M2
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| 4 |
All these choices are designed to accelerate convergence of iterative methods
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| 5 |
Anew = M1-1 A M2-1
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| 6 |
xnew = M2 x
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| 7 |
bnew = M1-1 b
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| 8 |
We choose M1 and M2 to make our standard methods perform better
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| 9 |
There are specialized preconditioning ideas and perhaps better general approaches such as multigrid and Incomplete LU (ILU) decomposition
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| 10 |
Anew xnew = bnew has same form as above and we can apply any of the methods that we used on A x = b
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