How to solve a linear system A * X = B when B and X are matrices instead as vectors?

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Hanna Liu 2021-4-22

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评论： Star Strider 2021-4-22

Sovling a linear system A * X = B when X and B are matrices. If I use lsqr，then B is required to be a vector.

I could also iterate for each column of the B matrix, but that is not very computationally efficient.

Matrix A is very big, so I could not save it explicitly. I could only use a function handle to compute A * X.

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Answer 1

Stephan 2021-4-22

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编辑：Stephan 2021-4-22

linsolve can handle this. From documentation (Input Arguments): "...If B is a matrix, then each column in the matrix represents a different vector for the right-hand side."

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Hanna Liu 2021-4-22

Thanks for the answer! My matrix A is very big. If I use linsolve, qr factorization is going to be slow and memory demanding. Is there a way to use an iterative solver similarly as lsqr?

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Answer 2

Star Strider 2021-4-22

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The lsqr function is primarily used for sparse systems. There are a number of other options for iterative solutions summarised in Iterative Methods for Linear Systems. I am not certain which (if any) of these would be appropriate to your problem.