Linear Systems
Routines
1.1 Linear Solvers
1.1.1 Solves a general system of linear equations Ax = b
LIN_SOL_GEN1.1.2 Solves a system of linear equations Ax = b,
where A is a self-adjoint matrix
LIN_SOL_SELF1.1.3 Solves a rectangular system of linear
equations Ax
≅ b, in a least-squares sense
LIN_SOL_LSQ1.1.4 Solves a rectangular least-squares system of linear
equations Ax
≅ b using singular value decomposition
LIN_SOL_SVD1.1.5 Solves multiple systems of linear equations
LIN_SOL_TRI1.1.6 Computes the singular value decomposition (SVD)
of a rectangular matrix, A
LIN_SVD1.2 Large-Scale Parallel Solvers
1.2.1 Parallel Constrained Least-Squares Solvers
1.3 Solution of Linear Systems, Matrix Inversion, and Q Determinant Evaluation
1.3.1 Real General Matrices
High accuracy linear system solution
LSARGSolves a linear system
LSLRGFactors and computes condition number
LFCRGSolves after factoring
LFSRGHigh accuracy linear system solution after factoring
LFIRGComputes determinant after factoring
LFDRG1.3.2 Complex General Matrices
High accuracy linear system solution
LSACGSolves a linear system
LSLCGFactors and computes condition number
LFCCGSolves a linear system after factoring
LFSCGHigh accuracy linear system solution after factoring
LFICGComputes determinant after factoring
LFDCG1.3.3 Real Triangular Matrices
Solves a linear system
LSLRTComputes condition number
LFCRTComputes determinant after factoring
LFDRT1.3.4 Complex Triangular Matrices
Solves a linear system
LSLCTComputes condition number
LFCCTComputes determinant after factoring
LFDCT1.3.5 Real Positive Definite Matrices
High accuracy linear system solution
LSADSSolves a linear system
LSLDSFactors and computes condition number
LFCDSSolve a linear system after factoring
LFSDSHigh accuracy linear system solution after factoring
LFIDSComputes determinant after factoring
LFDDS1.3.6 Real Symmetric Matrices
High accuracy linear system solution
LSASFSolves a linear system
LSLSFFactors and computes condition number
LFCSFSolves a linear system after factoring
LFSSFHigh accuracy linear system solution after factoring
LFISFComputes determinant after factoring
LFDSF1.3.7 Complex Hermitian Positive Definite Matrices
High accuracy linear system solution
LSADHSolves a linear system
LSLDHFactors and computes condition number
LFCDHSolves a linear system after factoring
LFSDHHigh accuracy linear system solution after factoring
LFIDHComputes determinant after factoring
LFDDH1.3.8 Complex Hermitian Matrices
High accuracy linear system solution
LSAHFSolves a linear system
LSLHFFactors and computes condition number
LFCHFSolves a linear system after factoring
LFSHFHigh accuracy linear system solution after factoring
LFIHFComputes determinant after factoring
LFDHF1.3.9 Real Band Matrices in Band Storage
Solves a tridiagonal system
LSLTRSolves a tridiagonal system: Cyclic Reduction
LSLCRHigh accuracy linear system solution
LSARBSolves a linear system
LSLRBFactors and compute condition number
LFCRBSolves a linear system after factoring
LFSRBHigh accuracy linear system solution after factoring
LFIRBComputes determinant after factoring
LFDRB1.3.10 Real Band Symmetric Positive Definite Matrices in Band Storage
High accuracy linear system solution
LSAQSSolves a linear system
LSLQSSolves a linear system
LSLPBFactors and computes condition number
LFCQSSolves a linear system after factoring
LFSQSHigh accuracy linear system solution after factoring
LFIQSComputes determinant after factoring
LFDQS1.3.11 Complex Band Matrices in Band Storage
Solves a tridiagonal system
LSLTQSolves a tridiagonal system: Cyclic Reduction
LSLCQHigh accuracy linear system solution
LSACBSolves a linear system
LSLCBFactors and computes condition number
LFCCBSolves a linear system after factoring
LFSCBHigh accuracy linear system solution after factoring
LFICBComputes determinant after factoring
LFDCB1.3.12 Complex Band Positive Definite Matrices in Band Storage
High accuracy linear system solution
LSAQHSolves a linear system
LSLQHSolves a linear system
LSLQBFactors and compute condition number
LFCQHSolves a linear system after factoring
LFSQHHigh accuracy linear system solution after factoring
LFIQHComputes determinant after factoring
LFDQH1.3.13 Real Sparse Linear Equation Solvers
Solves a sparse linear system
LSLXGSolves a linear system after factoring
LFSXG1.3.14 Complex Sparse Linear Equation Solvers
Solves a sparse linear system
LSLZGSolves a linear system after factoring
LFSZG1.3.15 Real Sparse Symmetric Positive Definite Linear Equation Solvers
Solves a sparse linear system
LSLXDSolves a linear system after factoring
LFSXD1.3.16 Complex Sparse Hermitian Positive Definite Linear Equation Solvers
Solves a sparse linear system
LSLZDSolves a linear system after factoring
LFSZD1.3.17 Real Toeplitz Matrices in Toeplitz Storage
Solves a linear system
LSLTO1.3.18 Complex Toeplitz Matrices in Toeplitz Storage
Solves a linear system
LSLTC1.3.19 Complex Circulant Matrices in Circulant Storage
Solves a linear system
LSLCC1.3.20 Iterative Methods
Preconditioned conjugate gradient
PCGRCJacobi conjugate gradient
JCGRCGeneralized minimum residual
GMRES1.4 Linear Least Squares and Matrix Factorization
1.4.1 Least Squares, QR Decomposition and Generalized Inverse
Solves a Least-squares system
LSQRRSolves a Least-squares system
LQRRVHigh accuracy Least squares
LSBRRLinearly constrained Least squares
LCLSQAccumulation of QR decomposition
LQERRQR decomposition Utilities
LQRSL1.4.2 Cholesky Factorization
Cholesky factoring for rank deficient matrices
LCHRGCholesky factor update
LUPCHCholesky factor down-date
LDNCH1.4.3 Singular Value Decomposition (SVD)
Real singular value decomposition
LSVRRComplex singular value decomposition
LSVCRGeneralized inverse
LSGRR