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I have implemented 1D mesh parallel QR decomposition and LU decomposition,I would like to ask if a linear equation Ax=b,b is a large matrix and I need to shard b or Shard A,b at the same time. Is there any math theory to do that?

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    $\begingroup$ What do you mean by "shard" when applied to a matrix? A quick google shows up nothing obviously useful $\endgroup$
    – Ian Bush
    Oct 15, 2023 at 10:00
  • $\begingroup$ Hi,Shard is split matrix as a block to N-process. for example, 1D Shard ,4-process:A = [A1,A2,A3,A4]. 2d-Shard 4-process: A = [[A1,A2],[A3,A4]. is equal to scalapack standard.So for a problem Ax =B,we need Shard B with LU or blocked-matrix. because B is very large.But I dont found a good theory to do it. $\endgroup$ Oct 15, 2023 at 12:32
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    $\begingroup$ If you are interested in Nvidia hardware have you looked at docs.nvidia.com/cuda/cusolvermp ? But reimplementing dense linear algebra routines can't be the way to go. I suspect explaining why what is available doesn't work for you might be more productive rather than doing it all over again. I have no idea what you mean by "factory-like" $\endgroup$
    – Ian Bush
    Oct 15, 2023 at 13:30
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    $\begingroup$ Like @IanBush, I don't understand what your goal is. Why would you re-implement a dense linear algebra library? Is your goal to develop new algorithms? Or to use such a library? $\endgroup$ Oct 16, 2023 at 15:10
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    $\begingroup$ @HaitaoXiao The thing is that you cannot have "simple", "transparent", "efficient", and "scalable" all at the same time. If that was possible, the people who write SLATE would have done that. $\endgroup$ Oct 16, 2023 at 22:01

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