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Help with Biconjugate Gradient to solve a system

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Old   December 5, 2003, 06:38
Default Help with Biconjugate Gradient to solve a system
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Hello to everybody: I have the following doubt: I want to solve the following system: Ax=f

I use an iterative solver, at first A is non-symmetric and positive. I use the Biconjugate gradient with A as preconditioner matrix.

Several iterations later, A gets to be negative in some of its elements and it is then when the program aborts. If I used a preconditioner matrix that was always symmetric and positive (for example a diagonal one like a lumped-mass matrix), would this problem disapear? What is the right solution?

Thank-you in advance. Best regards Isa
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Old   December 5, 2003, 14:51
Default Re: Help with Biconjugate Gradient to solve a syst
shobhit agarwal
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hi! for using a preconditioned conjugate gradient matrix there are three requirements. (1). The main(center)diagonal elements should never be zero. (2).The absolute value of the main diagonal element should be greater than all the values of the elements in that row.i.e. example abs(a22)>a2j (3).The signs of all the diagonal elements should be same and also matrix should be symmetric in terms of signs in your case since the sign of some elements of main diagonal change after a few iterations then the rule-3 gets violated hence the problem it seems that there is some formulation problem check that,because even if you use the preconditioned gradient method the requiremnt no.3 is there for more refference see MSIMSL library and particularly help files jcgrc. shobhit
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Old   December 20, 2003, 08:19
Default Re: Help with Biconjugate Gradient to solve a syst
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you should use GMRES or GPBiCG(m,l) linears solvers. these are two best general-purposed linear solvers.
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