Deferred correction for the integral equation eigenvalue problem
K. W. Chu,A. Spence +1 more
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In this paper, the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction is considered, and a convergence theorem is proved and a numerical example illustrating the theory is given.Abstract:
This paper considers the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction. A convergence theorem is proved and a numerical example illustrating the theory is given.read more
Citations
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On the numerical solution of nonlinear eigenvalue problems
TL;DR: The numerical solution of the nonlinear eigenvalue problemA(λ)x=0, where the matrixA( λ) is dependent on the eigen value parameter λ nonlinearly is considered.
Journal ArticleDOI
Refinement methods of Newton type for approximate eigenelements of integral operators
Mario Ahues,Mauricio Telias +1 more
TL;DR: In this article, the authors present in the context of Newton type methods six iterative techniques to refine approximate eigenelements of compact linear operators defined on a complex Banach space.
Journal ArticleDOI
Deferred Correction Methods for Ordinary Differential Equations
TL;DR: The theoretical underpinnings of deferred correction methods in a unified manner are reviewed, specifically the classical algorithm of Zadunaisky/Stetter, the method of Dutt, Greengard and Rokhlin, spectral deferred correction, and integral deferred correction.
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High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
TL;DR: Second order finite differences are applied to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain.
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Deferred correction for the ordinary differential equation eigenvalue problem
TL;DR: In this paper, the authors extended the deferred correction technique to deal with ordinary differential equation eigenvalue problems, where only the small eigenvalues and the corresponding eigenfunctions are considered.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
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A survey of numerical methods for the solution of Fredholm integral equations of the second kind
Lars B. Wahlbin,Kendall Atkinson +1 more
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Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
TL;DR: In this paper, a technique for obtaining error bounds for certain characteristic subspaces associated with the algebraic eigenvalue problem, the generalized eigen value problem, and the singular value decomposition is described.
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