Computing generalized Inverse of a square but sparse matrix?

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Sanwar Ahmad 2020-12-16

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回答： Christine Tobler 2021-1-8

I am trying to find the generalized inverse of a square and sparse matrix. I am using Matlab, however pinv(matrix) doesn't work for sparse matrices. If you have any suggestion or algorithm, please share. Thanks in advance.

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Answer 1

Rishabh Mishra 2020-12-21

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Hi,

The disadvantages of using ‘pinv’ to find inverse of sparse matrix are:

‘pinv’ requires costly SVD.
‘pinv’ does not work with sparse matrix.

Instead, you can use the function ‘pseudo-inverse’ for the same purpose. Refer the following link for documentation of ‘pseudo-inverse’ function.

Hope this helps!

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Answer 2

Christine Tobler 2021-1-8

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If you want to apply pinv(A)*b, you can instead use lsqminnorm(A, b), which also works for sparse matrices and does something equivalent (using QR decomposition instead of SVD).