GpBiCg Class

A Generalized Product Bi-Conjugate Gradient iterative matrix solver.

Inheritance Hierarchy

SystemObject
Altaxo.Calc.LinearAlgebra.Complex.SolversGpBiCg

Namespace: Altaxo.Calc.LinearAlgebra.Complex.Solvers
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)

Syntax

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public sealed class GpBiCg : IIterativeSolver<Complex>

The GpBiCg type exposes the following members.

Constructors

	Name	Description
	GpBiCg	Initializes a new instance of the GpBiCg class

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Properties

	Name	Description
	NumberOfBiCgStabSteps	Gets or sets the number of steps taken with the BiCgStab algorithm before switching over to the GPBiCG algorithm.
	NumberOfGpBiCgSteps	Gets or sets the number of steps taken with the GPBiCG algorithm before switching over to the BiCgStab algorithm.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	Solve	Solves the matrix equation Ax = b, where A is the coefficient matrix, b is the solution vector and x is the unknown vector.
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Remarks

The Generalized Product Bi-Conjugate Gradient (GPBiCG) solver is an alternative version of the Bi-Conjugate Gradient stabilized (CG) solver. Unlike the CG solver the GPBiCG solver can be used on non-symmetric matrices.
Note that much of the success of the solver depends on the selection of the proper preconditioner.

The GPBiCG algorithm was taken from:
GPBiCG(m,l): A hybrid of BiCGSTAB and GPBiCG methods with efficiency and robustness
S. Fujino
Applied Numerical Mathematics, Volume 41, 2002, pp 107 - 117

The example code below provides an indication of the possible use of the solver.

Reference

Altaxo.Calc.LinearAlgebra.Complex.Solvers Namespace