﻿ArnoldiEigenvalueSolver Class

# 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
`public class ArnoldiEigenvalueSolver`

The ArnoldiEigenvalueSolver type exposes the following members.

Constructors
NameDescription
ArnoldiEigenvalueSolver Constructs a SparseGeneralizedEigServer instance.
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Methods
NameDescription
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.