SolveLS-help: A Collection of Iterative Solvers for (Sparse) Linear System...
In SolveLS: Iterative Methods for Solving Linear System of Equations
Description
Non-square matrix
Support for Sparse Matrix
Composition of the Package
References
Description
Solving a system of linear equations is one of the most fundamental
computational problems for many fields of mathematical studies, such as
regression from statistics or numerical partial differential equations.
We provide a list of both stationary and nonstationary solvers. Sparse
matrix class from Matrix is also supported for large sparse system.
Non-square matrix
For a matrix A of size (m-by-n), we say the system is
overdetermined if m>n, underdetermined if m<n, or
squared if m=n. In the current version, underdetermined system is
not supported; it will later appear with sparse constraints. For an overdetermined system,
it automatically transforms the problem into normal equation, i.e.,
Ax=b \rightarrow A^T Ax = A^T b
even though if suffers from worse condition number while having desirable property
of a system to be symmetric and positive definite.
Support for Sparse Matrix
RcppArmadillo is extensively used in the package. In order for
bullet-proof transition between dense and sparse matrix, only 3 of
12 RcppArmadillo-supported sparse matrix formats have access to
our algorithms; "dgCMatrix","dtCMatrix" and "dsCMatrix".
Please see Dirk Eddelbuettel's
posting on sparse matrix support from RcppArmadillo. If either of two inputs A or b is
sparse, all matrices involved are automatically transformed into sparse matrices.
Composition of the Package
Following is a list of stationary methods,
lsolve.jacobiJacobi method
lsolve.gsGauss-Seidel method
lsolve.sorSuccessive Over-Relaxation method
lsolve.ssorSymmetric Successive Over-Relaxation method
as well as nonstationary (or, Krylov subspace) methods,
lsolve.bicgBi-Conjugate Gradient method
lsolve.bicgstabBi-Conjugate Gradient Stabilized method
lsolve.cgConjugate Gradient method
lsolve.cgsConjugate Gradient Squared method
lsolve.chebyChebyshev method
lsolve.gmresGeneralized Minimal Residual method
lsolve.qmrQuasi-Minimal Residual method
Also, aux.fisch is provided to generate a sparse system of
discrete Poisson matrix from finite difference approximation scheme of Poisson equation
on 2-dimensional square domain.
References
Demmel, J.W. (1997) Applied Numerical Linear Algebra, 1st ed., SIAM.
Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J.,
Eijkhout, V., Pozo, R., Romine, C., and van der Vorst, H. (1994) Templates for the Solution
of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. Philadelphia, SIAM.
SolveLS documentation built on Feb. 12, 2018, 5:03 p.m.
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Description Non-square matrix Support for Sparse Matrix Composition of the Package References
Description
Solving a system of linear equations is one of the most fundamental computational problems for many fields of mathematical studies, such as regression from statistics or numerical partial differential equations. We provide a list of both stationary and nonstationary solvers. Sparse matrix class from Matrix is also supported for large sparse system.
Non-square matrix
For a matrix A of size (m-by-n), we say the system is
overdetermined if m>n, underdetermined if m<n, or
squared if m=n. In the current version, underdetermined system is
not supported; it will later appear with sparse constraints. For an overdetermined system,
it automatically transforms the problem into normal equation, i.e.,
Ax=b \rightarrow A^T Ax = A^T b
even though if suffers from worse condition number while having desirable property of a system to be symmetric and positive definite.
Support for Sparse Matrix
RcppArmadillo is extensively used in the package. In order for
bullet-proof transition between dense and sparse matrix, only 3 of
12 RcppArmadillo-supported sparse matrix formats have access to
our algorithms; "dgCMatrix","dtCMatrix" and "dsCMatrix".
Please see Dirk Eddelbuettel's
posting on sparse matrix support from RcppArmadillo. If either of two inputs A or b is
sparse, all matrices involved are automatically transformed into sparse matrices.
Composition of the Package
Following is a list of stationary methods,
lsolve.jacobiJacobi method
lsolve.gsGauss-Seidel method
lsolve.sorSuccessive Over-Relaxation method
lsolve.ssorSymmetric Successive Over-Relaxation method
as well as nonstationary (or, Krylov subspace) methods,
lsolve.bicgBi-Conjugate Gradient method
lsolve.bicgstabBi-Conjugate Gradient Stabilized method
lsolve.cgConjugate Gradient method
lsolve.cgsConjugate Gradient Squared method
lsolve.chebyChebyshev method
lsolve.gmresGeneralized Minimal Residual method
lsolve.qmrQuasi-Minimal Residual method
Also, aux.fisch is provided to generate a sparse system of
discrete Poisson matrix from finite difference approximation scheme of Poisson equation
on 2-dimensional square domain.
References
Demmel, J.W. (1997) Applied Numerical Linear Algebra, 1st ed., SIAM.
Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and van der Vorst, H. (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. Philadelphia, SIAM.
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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