[petsc-users] Matrix equation involving square-root

[Jeff Steward]

I have a real SPD matrix A, and I would like to find x for

(A + A^{1/2})x = b

where A^{1/2} is the unique matrix such that A^{1/2}A^{1/2} = A. The
trouble is I don't have A^{1/2} (unless I compute the eigenpairs of A which
is fairly expensive), only A.

Is there a computationally efficient method in PETSc to find x in my case?
Ideally I would like to use an iterative method and a matrix shell for A
due to memory concerns and the fact that I don't need an exact solution.

Best wishes,

Jeff
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