Template Numerical Library: TNL::Solvers::Linear Namespace Reference

Template Numerical Library version\ main:0b2c40fb1

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TNL::Solvers::Linear Namespace Reference

Namespace for linear system solvers. More...

## Namespaces
namespace | Preconditioners
| Namespace for preconditioners of linear system solvers.

## Classes
class | BICGStab
| Iterative solver of linear systems based on the biconjugate gradient stabilized (BICGStab) method. More...
class | BICGStabL
| Iterative solver of linear systems based on the BICGStab(l) method. More...
class | CG
| Iterative solver of linear systems based on the conjugate gradient method. More...
class | CuDSSWrapper
class | CuSolverWrapper
class | GEM
| Gaussian Elimination Method (GEM) direct solver for dense linear systems. More...
class | GinkgoDirectSolver
class | GMRES
| Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method. More...
class | HypreBiCGSTAB
| Wrapper for the BiCGSTAB solver in Hypre. More...
class | HypreBoomerAMG
| Wrapper for the BoomerAMG solver/preconditioner in Hypre. More...
class | HypreDiagScale
| Wrapper for the Jacobi preconditioner in Hypre. More...
class | HypreEuclid
| Wrapper for the Euclid preconditioner in Hypre. More...
class | HypreFlexGMRES
| Wrapper for the Flexible GMRES solver in Hypre. More...
class | HypreGMRES
| Wrapper for the GMRES solver in Hypre. More...
class | HypreIdentity
| Wrapper for the identity operator as a Hypre solver. More...
class | HypreILU
| Wrapper for Hypre's native parallel ILU preconditioner. More...
class | HypreParaSails
| Wrapper for the ParaSails preconditioner in Hypre. More...
class | HyprePCG
| Wrapper for the PCG solver in Hypre. More...
class | HypreSolver
| Abstract class for Hypre's solvers and preconditioners. More...
class | HypreTriSolve
| Wrapper for Hypre's preconditioner that is intended for matrices that are triangular in some ordering. More...
class | IDRs
| Iterative solver of linear systems based on the IDR(s) method. More...
class | Jacobi
| Iterative solver of linear systems based on the Jacobi method. More...
struct | LinearResidueGetter
class | LinearSolver
| Base class for iterative solvers of systems of linear equations. More...
class | SOR
| Iterative solver of linear systems based on the Successive-overrelaxation (SOR) or Gauss-Seidel method. More...
class | TFQMR
| Iterative solver of linear systems based on the Transpose-free quasi-minimal residual (TFQMR) method. More...
struct | Traits
struct | Traits< Matrices::DistributedMatrix< Matrix > >
class | UmfpackWrapper

## Functions
template<bool fullStorage = true, typename Matrix, typename Vector1, typename Vector2>
void | triangularSolveLower (const Matrix &L, Vector1 &x, const Vector2 &b)
template<bool reversedRows = false, bool fullStorage = true, typename Matrix, typename Vector1, typename Vector2>
void | triangularSolveUpper (const Matrix &U, Vector1 &x, const Vector2 &b)

## Detailed Description

Namespace for linear system solvers.

This namespace contains the following algorithms and methods for solution of linear systems.

# Direct methods

# Iterative methods

## Stationary methods

1. Jacobi method - TNL::Solvers::Linear::Jacobi
2. Successive-overrelaxation method, SOR - TNL::Solvers::Linear::SOR

## Krylov subspace methods

1. Conjugate gradient method, CG - TNL::Solvers::Linear::CG
2. Biconjugate gradient stabilized method, BICGStab - TNL::Solvers::Linear::BICGStab
3. BICGStab(l) method - TNL::Solvers::Linear::BICGStabL
4. Transpose-free quasi-minimal residual method, TFQMR - TNL::Solvers::Linear::TFQMR
5. Generalized minimal residual method, GMERS - TNL::Solvers::Linear::GMRES with various methods of orthogonalization
   1. Classical Gramm-Schmidt, CGS
   2. Classical Gramm-Schmidt with reorthogonalization, CGSR
   3. Modified Gramm-Schmidt, MGS
   4. Modified Gramm-Schmidt with reorthogonalization, MGSR
   5. Compact WY form of the Householder reflections, CWY