Chapter 1 Linear Systems
Routines
Linear Solvers
Solves a general system of linear equations Ax = b
, LIN_SOL_GENSolves a system of linear equations Ax = b,
where A is a self-adjoint matrix
, LIN_SOL_SELFSolves a rectangular system of linear
equations Ax
≅ b, in a least-squares sense
, LIN_SOL_LSQSolves a rectangular least-squares system of linear
equations Ax
≅ b using singular value decomposition
, LIN_SOL_SVDSolves multiple systems of linear equations
, LIN_SOL_TRIComputes the singular value decomposition (SVD)
of a rectangular matrix,
, A
LIN_SVDLarge-Scale Parallel Solvers
Parallel Constrained Least-Squares Solvers
Solution of Linear Systems, Matrix Inversion, and Q Determinant Evaluation
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
, LFDRGComplex 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
, LFDCGReal Triangular Matrices
Solves a linear system
, LSLRTComputes condition number
, LFCRTComputes determinant after factoring
, LFDRTComplex Triangular Matrices
Solves a linear system
, LSLCTComputes condition number
, LFCCTComputes determinant after factoring
, LFDCTReal 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
, LFDDSReal 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
, LFDSFComplex 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
, LFDDHComplex 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
, LFDHFReal 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
, LFDRBReal 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
, LFDQSComplex 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
, LFDCBComplex 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
, LFDQHReal Sparse Linear Equation Solvers
Solves a sparse linear system
, LSLXGSolves a linear system after factoring
, LFSXGComplex Sparse Linear Equation Solvers
Solves a sparse linear system
, LSLZGSolves a linear system after factoring
, LFSZGReal Sparse Symmetric Positive Definite Linear Equation Solvers
Solves a sparse linear system
, LSLXDSolves a linear system after factoring
, LFSXDComplex Sparse Hermitian Positive Definite Linear Equation Solvers
Solves a sparse linear system
, LSLZDSolves a linear system after factoring
, LFSZDReal Toeplitz Matrices in Toeplitz Storage
Solves a linear system
, LSLTOComplex Toeplitz Matrices in Toeplitz Storage
Solves a linear system
, LSLTCComplex Circulant Matrices in Circulant Storage
Solves a linear system
, LSLCCIterative Methods
Preconditioned conjugate gradient
, PCGRCJacobi conjugate gradient
, JCGRCGeneralized minimum residual
, GMRESLinear Least Squares and Matrix Factorization
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
, LQRSLCholesky Factorization
Cholesky factoring for rank deficient matrices
, LCHRGCholesky factor update
, LUPCHCholesky factor down-date
, LDNCHSingular Value Decomposition (SVD)
Real singular value decomposition
, LSVRRComplex singular value decomposition
, LSVCRGeneralized inverse
, LSGRR