### Efficient computation (solve) of Ax = b when A is symmetric

Posted:

**Thu Oct 05, 2017 4:28 pm**Hello,

I want to solve a SPARSE linear system Ax = b and I know, A is always a symmetric matrix (structure & values). The size of the matrix is n = 40800, it's a sparse matrix of size n x n. (containing real, double values).

As the matrix is symmetric with respect to structure and values, there might be quite some efficiency gain (up to 50%) if:

I would only copy and transfer the upper or lower triangle to Magma (Note: A single simulation I do, requires 8000-10000 matrix transfers!)

AND

Apply magmablas_dsymmetrize() ... if it's applicable to sparse matrices in CSR format and fast?

OR

Set a "symmetry" marker if it's available in Magma and if Magma would solve a linear system based on that? (another library offers such an option)

How to solve a linear system with sparse symmetric matrices efficiently?

Klaus

I want to solve a SPARSE linear system Ax = b and I know, A is always a symmetric matrix (structure & values). The size of the matrix is n = 40800, it's a sparse matrix of size n x n. (containing real, double values).

As the matrix is symmetric with respect to structure and values, there might be quite some efficiency gain (up to 50%) if:

I would only copy and transfer the upper or lower triangle to Magma (Note: A single simulation I do, requires 8000-10000 matrix transfers!)

AND

Apply magmablas_dsymmetrize() ... if it's applicable to sparse matrices in CSR format and fast?

OR

Set a "symmetry" marker if it's available in Magma and if Magma would solve a linear system based on that? (another library offers such an option)

How to solve a linear system with sparse symmetric matrices efficiently?

Klaus