Get inverse of a huge matrix by inverting its submatrices
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Hi,
I need to calculate the inverse of a matrix i.e. 85000x85000 (later bigger), which I need to break down to submatrices to be able to store them (memory problem). Therefore, I would need to work with inverses of the submatrices to calculate the inverse of the matrix.
1) Is there a more efficient way to think about this problem in Matlab?
2) Are parts of these submatrix inversion problems already solved in available codes?
Thanks for your advice
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6 Comments
Walter Roberson
on 24 Jul 2016
I am not aware of any mathematical transformation that allows the calculation of an inverse of a matrix in terms of the inverses of submatrices -- only of calculations of the inverse in terms of the adjunct matrices.
Answers (1)
Steven Lord
on 24 Jul 2016
If you're inverting the matrix to try to solve a system of linear equations, consider using the iterative solvers like gmres and friends instead. If the problem is sparse and structured, you may not need to explicitly create the 85000-by-85000 matrix but instead write a function that computes the product of that matrix (and/or its transpose) with a vector.
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