Storing a symmetric matrix and calculating it's inverse.

1) Does MATLAB have a way to exploit symmetry of a known sparse matrix (in terms of storage of matrix elements) and calculate it's inverse in efficient way ?

Or

2) Does MATLAB have a way to exploit symmetry of sparse matrix for solving Ax = b, using x = A\b ,where A is a known symmetric matrix ?

Sparse storage does help, but it still does not take advantage of symmetry.

Answer 1

[Harshendra Shah]

For answering your first query, The computational complexity of sparse operations is proportional to nnz, the number of nonzero elements in the matrix. Computational complexity also depends linearly on the row size m and column size n of the matrix, but is independent of the product m*n, the total number of zero and nonzero elements.

For your queries on inverse of the sparse matrix and solving Ax = b you can go throgh the following documentation link for Sparse Matrix Operations:

https://in.mathworks.com/help/matlab/math/sparse-matrix-operations.html

This link will answer all your queries related to Sparse Matrix Operations in MATLAB.

For inverse of the sparse matrix, you can also go throgh the following File Exchange link which might be helpful:

https://in.mathworks.com/matlabcentral/fileexchange/33966-sparseinv-sparse-inverse-subset