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### IMSL Routines for Linear Systems

IMSL Routines for Linear Systems

## Matrix Inversion

IMSL_INV: General matrix inversion.

## Linear Equations with Full Matrices

IMSL_CHFAC: Factorization of symmetric positive definite matrices.

IMSL_CHSOL: Systems involving symmetric positive definite matrices.

IMSL_LUFAC: LU factorization of general matrices.

IMSL_LUSOL: Systems involving general matrices.

## Linear Least Squares with Full Matrices

IMSL_CHNNDFAC: Factor and generalized inverse for positive semidefinite matrices.

IMSL_CHNNDSOL: Solve and generalized inverse for positive semidefinite matrices.

IMSL_LINLSQ: Linear constraints.

IMSL_QRFAC: Least-squares factorization.

IMSL_QRSOL: Least-squares solution.

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

## Sparse Matrices

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

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

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

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

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

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

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

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

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

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

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

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