IterativeLinearSolvers module

Detailed Description

This module currently provides iterative methods to solve problems of the form A x = b, where A is a squared matrix, usually very large and sparse. Those solvers are accessible via the following classes:

• ConjugateGradient for selfadjoint (hermitian) matrices,
• LeastSquaresConjugateGradient for rectangular least-square problems,
• BiCGSTAB for general square matrices.

These iterative solvers are associated with some preconditioners:

• IdentityPreconditioner - not really useful
• DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
• IncompleteLUT - incomplete LU factorization with dual thresholding

Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport, AccelerateSupport.

#include <Eigen/IterativeLinearSolvers>

Classes
class	Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >
	A bi conjugate gradient stabilized solver for sparse square problems. More...
class	Eigen::ConjugateGradient< MatrixType_, UpLo_, Preconditioner_ >
	A conjugate gradient solver for sparse (or dense) self-adjoint problems. More...
class	Eigen::DiagonalPreconditioner< Scalar_ >
	A preconditioner based on the digonal entries. More...
class	Eigen::IdentityPreconditioner
	A naive preconditioner which approximates any matrix as the identity matrix. More...
class	Eigen::IncompleteLUT< Scalar_, StorageIndex_ >
	Incomplete LU factorization with dual-threshold strategy. More...
class	Eigen::IterativeSolverBase< Derived >
	Base class for linear iterative solvers. More...
class	Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >
	Jacobi preconditioner for LeastSquaresConjugateGradient. More...
class	Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >
	A conjugate gradient solver for sparse (or dense) least-square problems. More...
class	Eigen::SolveWithGuess< Decomposition, RhsType, GuessType >
	Pseudo expression representing a solving operation. More...