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 Post subject: Solving systems of linear equations
PostPosted: Tue May 25, 2010 8:02 am 
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Joined: Sun May 16, 2010 11:42 pm
Posts: 63
Am I right in thinking that the densesolver unit would have the best functions for solving systems of linear equations (which may or may not be symmetrical)?

My application (initially) will be structural analysis, i.e. systems of beams subject to known loads and/or deflections. Any hints on the best way to tackle it with the AlgLib fucntions?

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 Post subject: Re: Solving systems of linear equations
PostPosted: Tue May 25, 2010 8:45 am 
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Joined: Fri May 07, 2010 7:06 am
Posts: 878
Yes, densesolver will contain all new code for general/SPD linear solvers. As for symmetric indefinite solvers, situation is less clear.

ALGLIB has rudimentary support for symmetric indefinite systems (LDLT real solver), but I am unsatisfied with its performance, and I should say that it is really hard to optimize LDLT decomposition code (a lot of permutations, low rank updates - it is unsuited for almost all optimizations). It is possible, but just too hard. So I think that it is better to optimize LU-based solver and to use it for symmetric matrices. Maybe LDLT solver will be dropped in one of the following releases.

Returning to your question, I recommend to use densesolver unit for any kind of system you'll try to solve. General and indefinite systems may be solved with LU-based solver, SPD system - with Cholesky-based solver.


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 Post subject: Re: Solving systems of linear equations
PostPosted: Thu May 07, 2015 6:19 am 
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Joined: Tue Apr 28, 2015 5:22 am
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I think that it is better to optimize LU-based solver and to use it for symmetric matrices.

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