iterative solvers and speed comparisons

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James McDaniel 2013-4-24

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https://ww2.mathworks.cn/matlabcentral/answers/73401-iterative-solvers-and-speed-comparisons

We are using an iterative solver with various starting guesses and trying to assess whether this is faster than using a direct solve. However, the iterative solvers seem to be about an order of magnitude slower even when the initial guess is very accurate. In fact, using the solution from a direct solve (backslash) in an iterative solver takes about 10 times longer than the direct solve did. We suspect this is because the iterative solvers are not compiled and linked and the direct solver is. Can anyone recommend accurate ways of comparing iterative solvers to direct solvers for speed/efficiency within matlab? We would like to predict performance in a fully compiled language like C++ or fortran. Thank you.

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Matt J 2013-4-24

编辑：Matt J 2013-4-24

We need a lot more details about the tests you did, e.g., the equations being solved and which solvers were used.

In fact, using the solution from a direct solve (backslash) in an iterative solver takes about 10 times longer than the direct solve did.

That sounds like a symptom of ill-conditioning. There are many non-unique solutions to your equations (or approximately so), so the iterative solver spends its time crawling along a locus of nearly equivalent solutions, unable to decide between them until some stopping criterion is finally met.

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