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Sunday, July 26, 2020 | History

4 edition of Estimating eigenvalues with a posteriori/a priori inequalities found in the catalog.

Estimating eigenvalues with a posteriori/a priori inequalities

by J. R. Kuttler

  • 133 Want to read
  • 34 Currently reading

Published by Pitman Advanced Pub. Program in Boston .
Written in English

    Subjects:
  • Operator equations -- Numerical solutions.,
  • Eigenvalues.,
  • Inequalities (Mathematics)

  • Edition Notes

    StatementJ.R. Kuttler & V.G. Sigillito.
    SeriesResearch notes in mathematics ;, 135
    ContributionsSigillito, V. G., 1937-
    Classifications
    LC ClassificationsQA374 .K95 1985
    The Physical Object
    Pagination152 p. :
    Number of Pages152
    ID Numbers
    Open LibraryOL2531657M
    ISBN 100273086995
    LC Control Number85012294

    the i-th eigenvalue error, the associated eigenvector energy error, and the dual norm of the residual. We extend them in an appendix to the generic class of bounded-below self-adjoint operators with compact resolvent. Key words: Laplace eigenvalue problem, a posteriori estimate, guaranteed eigenvalue bound, guaranteed. () A posteriori estimates for the Stokes eigenvalue problem. Numerical Methods for Partial Differential Equations , () On the number of reliable finite-element eigenmodes.

    Table of contents ix Efficiency of element and face residuals via the bubble functions technique 85 Efficiency of jumps terms via local Neumann problems. The automated multilevel substructuring (AMLS) method has been developed to reduce the computational demands of frequency response analysis and has recently been proposed as an alternative to iterative projection methods like those of Lanczos or Jacobi--Davidson for computing a large number of eigenvalues for matrices of very large dimension.

    Let be an approximation for, where is not an eigenvalue of, and with. Suppose that ; and, for, where is the separation constant of the eigenvalue ; satisfy Then. Let be a positive constant satisfying the following inequalities: Condition 6. In? 12 thro we review numerical methods for estimating the eigenvalues and eigenfunctions. Rayleigh-Ritz, finite elements, intermediate methods, finite differ-ences, point matching, a posteriori-a priori inequalities, Galerkin, and other methods are discussed. We have especially included references to papers containing specific.


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Estimating eigenvalues with a posteriori/a priori inequalities by J. R. Kuttler Download PDF EPUB FB2

Get this from a library. Estimating eigenvalues with a posteriori/a priori inequalities. [J R Kuttler; V G Sigillito] -- This Research Note presents a method for the numerical estimation of eigenvalues which is easy to understand, practical to implement and effective in its results.

It is developed with complete. Get this from a library. Estimating eigenvalues with a posteriori a priori inequalities.

[J R Kuttler; Vincent G Sigillito]. Author of Estimating eigenvalues with a posteriori / a priori inequalities. Open Library is an initiative of the Internet Archive, a (c)(3) non-profit, building a digital library of Internet sites and other cultural artifacts in digital projects include.

Cite this chapter as: Reginska T. () An Iteration Method of Improving Computable Bounds for Eigenvalues. In: Albrecht J., Collatz L., Velte W., Wunderlich W. (eds) Numerical Treatment of Eigenvalue Problems Vol.4 / Numerische Behandlung von Eigenwertaufgaben Band : Teresa Reginska.

Karhunen-Loéve transform: The b i are the eigenvectors sorted according to the eigenvalue. Stationarity: If X ij is the pixel value at location (i, j) then we enforce the equality E X i j X kl = C S k − i, l − j by estimating C S (a, b) from the true correlations and then using these values in the correlation system is the eigenvector system of the correlation matrix.

Journals & Books; Help Download full J. KUTTLER AND V. SIGILLITO, Estimating Eigenvalues with A Posteriori/A Priori Inequalities, in "Pitman Research Notes in Mathematics Series," Vol.Longman Sei. Tech., Harlow, 6. LEVINE AND G. LIEBERMAN, Quenching of solutions of parabolic equations with nonlinear boundary.

Abstract. This paper discusses spectral and spectral element methods with Legendre-Gauss-Lobatto nodal basis for general 2nd-order elliptic eigenvalue problems.

We give eigenvalue inclusion theorems allowing the computation of both-sided Stekloff-eigenvalue bounds from a given approximate eigenpair. We demonstrate in numerical examples the possibility to get close bounds for even higher eigenvalues using the boundary collocation method.

A good choice for trial functions are singularity functions allowing a control for the numerical stability and—in. Kuttler, J.R., Sigillito, V.G. () Estimating eigenvalues with a posteriori/a priori inequalities, Pitman, Boston-London-Melbourne Google Scholar [10] Lehman, S.R.

() Developments at an analytic corner of solutions of elliptic partial differential equations, J. of. Eigenvalues and spectra of molecules: Reed and Simon (, M), Vol. 4, Thirring (, M), Vol. Google Scholar Eigenvalue criteria for minima in the calculus of variations: Klötzler (, M).

INTRODUCTION This paper is one of a continuing series of studies of plate problems by the method of a posteriori-a priori inequalities. In this method an a posteriori eigenvalue inequality is combined with an appropriate a priori inequality to obtain lower and upper bounds for the vibrational frequencies in terms of integrals of known trial.

Estimating eigenvalues with a posteriori/a priori inequalities. This book is devoted to mathematical foundations of different formulations of problems on vibrations of periodic structures in.

Key words: Laplace eigenvalue problem, a posteriori estimate, eigenvalue error, eigenvector error, guar-anteed bound, conforming nite element method, inexact solver, stopping criteria 1 Introduction Precise numerical approximation of eigenvalues and eigenvectors is crucial in.

Article Tools. Add to my favorites. Download Citations. Remark As a conse quence of the pr evious theorem and the a priori estimate the last inequality b ec ause of A posteriori err or estimates for eigenvalue problems G.

Inspired by, and, we put into evidence a strategy that starts from a local Mourre inequality with respect to a conjugate operator (that is not supposed to be self-adjoint) and produces a local weighted estimation; from this, a cut-off procedure (both on the test function and on the weights,) leads to a Hardy type estimation and a simple.

Fig. 3, Fig. 4 show the adaptively refined meshes obtained with VEM and FEM procedures, respectively. Download: Download high-res image (77KB) Download: Download full-size image Fig.

Sloshing in a square domain. The method of a priori-a posteriori inequalities that can be used for computation of lower bounds on eigenvalues was described and published in [22, 23, 35].

However, in these original publications C2-continuous test and trial functions have been used in order to compute the actual lower bound. These functions are di cult to work with. Some Inequalities for the Eigenvalues of the Product of Positive Semidefinite Hermitian Matrices Boying Wang and Fuzhen Zhang* Department of Mathematics Beijing Normal University Beijing, People's Republic of China Submitted by George P.

Sty an ABSTRACT Let A1(A) > > AA) denote the eigenvalues of a Hermitian n by n matrix A, and let 1 _. We present a general numerical method for computing guaranteed two-sided bounds for principal eigenvalues of symmetric linear elliptic differential operators.

The approach is based on the Galerkin method, on the method of a priori--a posteriori inequalities, and on a complementarity technique. Yuping Zeng's 11 research works with 31 citations and reads, including: Convergence analysis of a modified weak Galerkin finite element method for Signorini and obstacle problems: MWG For.on the size of the eigenvalue or the convection coe cient.

1. Introduction While the numerical approximation of eigenvalues of symmetric second-order elliptic partial di erential equations (PDEs) with real eigen-pairs is relatively well understood, much less is known about non-symmetric problems with possibly complex eigenvalues.

A posteriori.A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.