# Tag Info

4

I do not know anything about the specific problem, but you might want to look into the techniques the "SParse Approximate Inverse (SPAI)" community has come up with over the past two decades. There, one is looking for a matrix $B \approx A^{-1}$ so that $\|BA-I\|$ is minimized (with regard to some norm, typically the Frobenius norm) and requiring ...

3

One reason why there might not be much research on this is that one usually avoids sparse matrix multiplications as much as possible in the first place. When applying the product to a vector $ABv$, you can associate from the right $A(Bv)$, and when solving linear systems you can add auxiliary variables to avoid forming the product; for instance, turn \$c = ...

2

I think there’s some confusion here. There’s no matrix and corresponding preconditioner. The latter are usually derived mechanically on the fly as the iterative scheme evolves unless you already have the matrix inverse, which would be the perfect preconditioner as you’d just apply the inverse and the iterative method would converge on its first step. The ...

5

Generally, preconditioners are considered to be part of the solver, so they are not included in test matrix collections. In fact, preconditioners are rarely constructed as an explicit matrix, making it hard to include them in a programming-language-agnostic manner. If you're using an existing sparse linear algebra framework or a language like MATLAB or ...

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