# Linear Systems Routines

## Matrix Inversion

IMSL_INV—General matrix inversion.

## Linear Equations with Full Matrices

IMSL_LUSOL—Systems involving general matrices.

IMSL_LUFAC—LU factorization of general matrices.

IMSL_CHSOL—Systems involving symmetric positive definite matrices.

IMSL_CHFAC—Factorization of symmetric positive definite matrices.

## Linear Least Squares with Full Matrices

IMSL_QRSOL—Least-squares solution.

IMSL_QRFAC—Least-squares factorization.

IMSL_SVDCOMP—Singular Value Decomposition (SVD) and generalized inverse.

IMSL_CHNNDSOL—Solve and generalized inverse for positive semidefinite matrices.

IMSL_CHNNDFAC—Factor and generalized inverse for positive semidefinite matrices.

IMSL_LINLSQ—Linear constraints.

## Sparse Matrices

IMSL_SP_LUSOL—Solve a sparse system of linear equations Ax = b.

IMSL_SP_LUFAC—Compute an LU factorization of a sparse matrix stored in either coordinate format or CSC format.

IMSL_SP_BDSOL—Solve a general band system of linear equations Ax = b.

IMSL_SP_BDFAC—Compute the LU factorization of a matrix stored in band storage mode.

IMSL_SP_PDSOL—Solve a sparse symmetric positive definite system of linear equations Ax = b.

IMSL_SP_PDFAC—Compute a factorization of a sparse symmetric positive definite system of linear equations Ax = b.

IMSL_SP_BDPDSOL—Solve a symmetric positive definite system of linear equations Ax = b in band symmetric storage mode.

IMSL_SP_BDPDFAC—Compute the RTR Cholesky factorization of symmetric positive definite matrix, A, in band symmetric storage mode.

IMSL_SP_GMRES—Solve a linear system Ax = b using the restarted generalized minimum residual (GMRES) method.

IMSL_SP_CG—Solve a real symmetric definite linear system using a conjugate gradient method.

IMSL_SP_MVMUL—Compute a matrix-vector product involving a sparse matrix and a dense vector.