ArnoldiEigenvalueSolver Class

Solve the generalized eigenvalue problem Ax = Mx(lambda) Where A is sparse symmetric and M is sparse symmetric semi position definite. Solve is accomplished using a shift and invert spectral transformation and implicitly restarted Arnoldi iteration.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreArnoldiEigenvalueSolver

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

C++

Copy

public class ArnoldiEigenvalueSolver

Public Class ArnoldiEigenvalueSolver

public ref class ArnoldiEigenvalueSolver

type ArnoldiEigenvalueSolver = class end

The ArnoldiEigenvalueSolver type exposes the following members.

Constructors

	Name	Description
	ArnoldiEigenvalueSolver	Constructs a SparseGeneralizedEigServer instance.

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Methods

	Name	Description
	Solve(DoubleSymCsrSparseMatrix, DoubleSymCsrSparseMatrix, ArnoldiEigenvalueOptions)	Solve the generalized symmetric eigenvalue problem Ax = Mx(lambda) using Arnoldi iteration, Where A is symmetric and M is symmetric positive semi-definite.
	Solve(DoubleSymmetricMatrix, DoubleSymmetricMatrix, ArnoldiEigenvalueOptions)	Solve the generalized egivenvalue problem Ax = Mx(lambda) Where A is sparse symmetric and M is sparse symmetric semi position definite. Solve is accomplished using a shift and invert spectral transformation and implicitly restarted Arnoldi iteration.

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Remarks

The shift and invert problem is inv(A - (sigma)M)Mx = x(nu), where nu = 1/(lambda - sigma). The transformation is effective for finding eigenvalues near sigma.

Reference

CenterSpace.NMath.Core Namespace