# Package spai: Information

**Source package:**spai

**Version:**3.2-alt9

**Build time:**Jan 15, 2024, 05:25 PM

**Category:**Sciences/Mathematics

**License:**GPLv2

**Summary:**SParse Approximate Inverse Preconditioner

**Description:**

Given a sparse matrix A the SPAI Algorithm computes a sparse approximate inverse M by minimizing || AM - I || in the Frobenius norm. The approximate inverse is computed explicitly and can then be applied as a preconditioner to an iterative method. The sparsity pattern of the approximate inverse is either fixed a priori or captured automatically: * Fixed sparsity: The sparsity pattern of M is either banded or a subset of the sparsity pattern of A. * Adaptive sparsity: The algorithm proceeds until the 2-norm of each column of AM-I is less than eps. By varying eps the user controls the quality and the cost of computing the preconditioner. Usually the optimal eps lies between 0.5 and 0.7. A very sparse preconditioner is very cheap to compute but may not lead to much improvement, while if M becomes rather dense it becomes too expensive to compute. The optimal preconditioner lies between these two extremes and is problem and computer architecture dependent. The approximate inverse M can also be used as a robust (parallel) smoother for (algebraic) multi-grid methods.

**List of rpms provided by this srpm:**

libspai (loongarch64)

libspai-debuginfo (loongarch64)

libspai-devel (loongarch64)

libspai-devel-doc (noarch)

spai (loongarch64)

spai-debuginfo (loongarch64)

**Maintainer:**Eugeny A. Rostovtsev

## Last changed

Sept. 22, 2021 Grigory Ustinov 3.2-alt9

- Fixed FTBFS.

Sept. 17, 2020 Grigory Ustinov 3.2-alt8

- Fixed FTBFS.

Aug. 12, 2012 Eugeny A. Rostovtsev 3.2-alt7

- Built with OpenBLAS instead of GotoBLAS2