FNLMath : Linear Systems
Linear Systems
Routines
Linear Solvers
Solves a general system of linear equations Ax = b LIN_SOL_GEN
Solves a system of linear equations Ax = b,
where A is a self-adjoint matrix LIN_SOL_SELF
Solves a rectangular system of linear
equations Ax  b, in a least-squares sense LIN_SOL_LSQ
Solves a rectangular least-squares system of linear
equations Ax b using singular value decomposition LIN_SOL_SVD
Solves multiple systems of linear equations LIN_SOL_TRI
Computes the singular value decomposition (SVD)
of a rectangular matrix, A LIN_SVD
Large-Scale Parallel Solvers
Parallel Constrained Least-Squares Solvers
Solves a linear, non-negative constrained
least-squares system PARALLEL_NONNEGATIVE_LSQ
Solves a linear least-squares system
with bounds on the unknowns PARALLEL_BOUNDED_LSQ
Solution of Linear Systems, Matrix Inversion, and Q Determinant Evaluation
Real General Matrices
High accuracy linear system solution LSARG
Solves a linear system LSLRG
Factors and computes condition number LFCRG
Factors LFTRG
Solves after factoring LFSRG
High accuracy linear system solution after factoring LFIRG
Computes determinant after factoring LFDRG
Inverts LINRG
Complex General Matrices
High accuracy linear system solution LSACG
Solves a linear system LSLCG
Factors and computes condition number LFCCG
Factors LFTCG
Solves a linear system after factoring LFSCG
High accuracy linear system solution after factoring LFICG
Computes determinant after factoring LFDCG
Inverts LINCG
Real Triangular Matrices
Solves a linear system LSLRT
Computes condition number LFCRT
Computes determinant after factoring LFDRT
Inverts LINRT
Complex Triangular Matrices
Solves a linear system LSLCT
Computes condition number LFCCT
Computes determinant after factoring LFDCT
Inverts LINCT
Real Positive Definite Matrices
High accuracy linear system solution LSADS
Solves a linear system LSLDS
Factors and computes condition number LFCDS
Factors LFTDS
Solve a linear system after factoring LFSDS
High accuracy linear system solution after factoring LFIDS
Computes determinant after factoring LFDDS
Inverts LINDS
Real Symmetric Matrices
High accuracy linear system solution LSASF
Solves a linear system LSLSF
Factors and computes condition number LFCSF
Factors LFTSF
Solves a linear system after factoring LFSSF
High accuracy linear system solution after factoring LFISF
Computes determinant after factoring LFDSF
Complex Hermitian Positive Definite Matrices
High accuracy linear system solution LSADH
Solves a linear system LSLDH
Factors and computes condition number LFCDH
Factors LFTDH
Solves a linear system after factoring LFSDH
High accuracy linear system solution after factoring LFIDH
Computes determinant after factoring LFDDH
Complex Hermitian Matrices
High accuracy linear system solution LSAHF
Solves a linear system LSLHF
Factors and computes condition number LFCHF
Factors LFTHF
Solves a linear system after factoring LFSHF
High accuracy linear system solution after factoring LFIHF
Computes determinant after factoring LFDHF
Real Band Matrices in Band Storage
Solves a tridiagonal system LSLTR
Solves a tridiagonal system: Cyclic Reduction LSLCR
High accuracy linear system solution LSARB
Solves a linear system LSLRB
Factors and compute condition number LFCRB
Factors LFTRB
Solves a linear system after factoring LFSRB
High accuracy linear system solution after factoring LFIRB
Computes determinant after factoring LFDRB
Real Band Symmetric Positive Definite Matrices in Band Storage
High accuracy linear system solution LSAQS
Solves a linear system LSLQS
Solves a linear system LSLPB
Factors and computes condition number LFCQS
Factors LFTQS
Solves a linear system after factoring LFSQS
High accuracy linear system solution after factoring LFIQS
Computes determinant after factoring LFDQS
Complex Band Matrices in Band Storage
Solves a tridiagonal system LSLTQ
Solves a tridiagonal system: Cyclic Reduction LSLCQ
High accuracy linear system solution LSACB
Solves a linear system LSLCB
Factors and computes condition number LFCCB
Factors LFTCB
Solves a linear system after factoring LFSCB
High accuracy linear system solution after factoring LFICB
Computes determinant after factoring LFDCB
Complex Band Positive Definite Matrices in Band Storage
High accuracy linear system solution LSAQH
Solves a linear system LSLQH
Solves a linear system LSLQB
Factors and compute condition number LFCQH
Factors LFTQH
Solves a linear system after factoring LFSQH
High accuracy linear system solution after factoring LFIQH
Computes determinant after factoring LFDQH
Real Sparse Linear Equation Solvers
Solves a sparse linear system LSLXG
Factors LFTXG
Solves a linear system after factoring LFSXG
Complex Sparse Linear Equation Solvers
Solves a sparse linear system LSLZG
Factors LFTZG
Solves a linear system after factoring LFSZG
Real Sparse Symmetric Positive Definite Linear Equation Solvers
Solves a sparse linear system LSLXD
Symbolic Factor LSCXD
Computes Factor LNFXD
Solves a linear system after factoring LFSXD
Complex Sparse Hermitian Positive Definite Linear Equation Solvers
Solves a sparse linear system LSLZD
Computes Factor LNFZD
Solves a linear system after factoring LFSZD
Real Toeplitz Matrices in Toeplitz Storage
Solves a linear system LSLTO
Complex Toeplitz Matrices in Toeplitz Storage
Solves a linear system LSLTC
Complex Circulant Matrices in Circulant Storage
Solves a linear system LSLCC
Iterative Methods
Generalized minimum residual GMRES
Partial Singular Value Decomposition ARPACK_SVD
Linear Least Squares and Matrix Factorization
Least Squares, QR Decomposition and Generalized Inverse
Solves a Least-squares system LSQRR
Solves a Least-squares system LQRRV
High accuracy Least squares LSBRR
Linearly constrained Least squares LCLSQ
QR decomposition LQRRR
Accumulation of QR decomposition LQERR
QR decomposition Utilities LQRSL
QR factor update LUPQR
Cholesky Factorization
Cholesky factoring for rank deficient matrices LCHRG
Cholesky factor update LUPCH
Cholesky factor down-date LDNCH
Singular Value Decomposition (SVD)
Real singular value decomposition LSVRR
Complex singular value decomposition LSVCR
Generalized inverse LSGRR