# Sparse Matrices: Direct Methods

Several routines employ direct methods (as opposed to iterative methods) for solving problems involving sparse matrices.

For general sparse linear systems, IMSL_SP_LUFAC and IMSL_SP_LUSOL form a factor/solve function pair. If a sparse matrix the problem Ax = b is to be solved for a single A, but multiple right-hand sides, b, then IMSL_SP_LUFAC should first be used to compute an LU decomposition of A, then follow multiple calls to IMSL_SP_LUSOL (one for each right-hand side, b). If only one right-hand side, b, is involved then IMSL_SP_LUSOL can be called directly, in which case the factor step is computed internally by IMSL_SP_LUSOL.

For general banded systems, IMSL_SP_BDSOL and IMSL_SP_BDFAC form a factor/solve pair. The relationship between SP_BSFAC and IMSL_SP_BDSOL is similar to that of IMSL_SP_LUFAC and IMSL_SP_LUSOL.

The functions IMSL_SP_PDFAC and IMSL_SP_PDSOL are provided for working with systems involving sparse symmetric positive definite matrices. The relationship between IMSL_SP_PDFAC and IMSL_SP_PDSOL is similar to that of IMSL_SP_LUFAC and IMSL_SP_LUSOL.

The functions SP_BDDFAC and IMSL_SP_BDPDSOL are provided for working with systems involving banded symmetric positive definite matrices. The relationship between IMSL_SP_BDPDFAC and IMSL_SP_BDPDSOL is similar to that of IMSL_SP_LUFAC and IMSL_SP_LUSOL.

- IMSL_SP_LUFAC—LU factorization of general matrices.
- IMSL_SP_LUSOL—Systems involving general matrices.
- IMSL_SP_BDFAC—LU factorization of band matrices.
- IMSL_SP_BDSOL—Systems involving band matrices.
- IMSL_SP_PDFAC—Factorization of symmetric positive definite matrices.
- IMSL_SP_PDSOL—Systems involving symmetric positive definite matrices.
- IMSL_SP_BDPDFAC—Cholesky factorization of symmetric positive definite matrices in band symmetric storage mode.
- IMSL_SP_BDPDSOL— Systems involving symmetric positive definite matrices in band symmetric storage mode