Template Numerical Library version\ main:eacc201d
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Namespaces | Classes | Functions
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  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 > >
 

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