Linear Systems

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

Preconditioned conjugate gradient PCGRC

Jacobi conjugate gradient JCGRC

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