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I am looking for a two things while calculating the large array matrix equation:

1) To increase the precision in simple LinearSolve function.

2) To find a way to parallelize the computation on all cores because the LinearSolve is called each time in a iteration process.

Is there way to decrease a computational time in case of LinearSolve? Probably, in my case this is a iterative process, so I would like to parallelize the operations on all cores. Another question is about precision. How can I increase the accurate of obtained results in LinearSolve, for example simple LinearSolve[a,b,WorkingPrecision->50] does not work of course because it is symbolic computation. But some suggestions?

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  • $\begingroup$ A detail you forgot to mention: is your matrix dense or sparse? $\endgroup$ – J. M. will be back soon May 18 '15 at 13:25
  • $\begingroup$ This is extremely confusing. If you have a symbolic rather than numeric matrix, what do you expect to do with precision? If the matrix is numeric, the remark "it is symbolic computation" does not give much of an idea as to what is the nature of the matrix entries. This question really needs a lot more detail in order to get any sensible suggestions. $\endgroup$ – Daniel Lichtblau May 18 '15 at 18:02
  • $\begingroup$ @DanielLichtblau: Assuming that numeric computation is needed, How one can improve the run time by parallelizing? $\endgroup$ – H. R. Jun 6 '17 at 10:33
  • $\begingroup$ Did you figure out any specific solutions? $\endgroup$ – H. R. Jun 6 '17 at 12:07
  • $\begingroup$ If the problem involves working with machine doubles on dense matrices then LinearSolve will use Lapack library code, which uses vendor-supplied BLAS, which often is parallelized. If the matrix is an explicit SparseArray then different methods might be used and I do not know if parallelization happens (or even if it is feasible) under the hood. $\endgroup$ – Daniel Lichtblau Jun 6 '17 at 14:53

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