FNLMath : Linear Systems
Linear Systems
Routines
1.1 Linear Solvers
1.1.1 Solves a general system of linear equations Ax = b LIN_SOL_GEN
1.1.2 Solves a system of linear equations Ax = b,
where A is a self-adjoint matrix LIN_SOL_SELF
1.1.3 Solves a rectangular system of linear
equations Ax  b, in a least-squares sense LIN_SOL_LSQ
1.1.4 Solves a rectangular least-squares system of linear
equations Ax b using singular value decomposition LIN_SOL_SVD
1.1.5 Solves multiple systems of linear equations LIN_SOL_TRI
1.1.6 Computes the singular value decomposition (SVD)
of a rectangular matrix, A LIN_SVD
1.2 Large-Scale Parallel Solvers
1.2.1 Parallel Constrained Least-Squares Solvers
1.2.2 Solves a linear, non-negative constrained
least-squares system PARALLEL_NONNEGATIVE_LSQ
1.2.3 Solves a linear least-squares system
with bounds on the unknowns PARALLEL_BOUNDED_LSQ
1.3 Solution of Linear Systems, Matrix Inversion, and Q Determinant Evaluation
1.3.1 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
1.3.2 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
1.3.3 Real Triangular Matrices
Solves a linear system LSLRT
Computes condition number LFCRT
Computes determinant after factoring LFDRT
Inverts LINRT
1.3.4 Complex Triangular Matrices
Solves a linear system LSLCT
Computes condition number LFCCT
Computes determinant after factoring LFDCT
Inverts LINCT
1.3.5 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
1.3.6 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
1.3.7 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
1.3.8 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
1.3.9 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
1.3.10 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
1.3.11 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
1.3.12 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
1.3.13 Real Sparse Linear Equation Solvers
Solves a sparse linear system LSLXG
Factors LFTXG
Solves a linear system after factoring LFSXG
1.3.14 Complex Sparse Linear Equation Solvers
Solves a sparse linear system LSLZG
Factors LFTZG
Solves a linear system after factoring LFSZG
1.3.15 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
1.3.16 Complex Sparse Hermitian Positive Definite Linear Equation Solvers
Solves a sparse linear system LSLZD
Computes Factor LNFZD
Solves a linear system after factoring LFSZD
1.3.17 Real Toeplitz Matrices in Toeplitz Storage
Solves a linear system LSLTO
1.3.18 Complex Toeplitz Matrices in Toeplitz Storage
Solves a linear system LSLTC
1.3.19 Complex Circulant Matrices in Circulant Storage
Solves a linear system LSLCC
1.3.20 Iterative Methods
Preconditioned conjugate gradient PCGRC
Jacobi conjugate gradient JCGRC
Generalized minimum residual GMRES
Partial Singular Value Decomposition ARPACK_SVD
1.4 Linear Least Squares and Matrix Factorization
1.4.1 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
1.4.2 Cholesky Factorization
Cholesky factoring for rank deficient matrices LCHRG
Cholesky factor update LUPCH
Cholesky factor down-date LDNCH
1.4.3 Singular Value Decomposition (SVD)
Real singular value decomposition LSVRR
Complex singular value decomposition LSVCR
Generalized inverse LSGRR
Published date: 03/19/2020
Last modified date: 03/19/2020