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Thursday, May 7, 2020 | History

7 edition of The symmetric eigenvalue problem found in the catalog.

The symmetric eigenvalue problem

by Beresford N. Parlett

  • 183 Want to read
  • 4 Currently reading

Published by Prentice-Hall in Englewood Cliffs, N.J .
Written in English

    Subjects:
  • Symmetric matrices.,
  • Eigenvalues.

  • Edition Notes

    StatementBeresford N. Parlett.
    SeriesPrentice-Hall series in Computational Mathematics
    Classifications
    LC ClassificationsQA188 .P37
    The Physical Object
    Paginationxix, 348 p. :
    Number of Pages348
    ID Numbers
    Open LibraryOL4422740M
    ISBN 100138800472
    LC Control Number79027221

    In Matrix Computations by Golub and Van Loan (3rd edition, page ) an algorithm is given for a parallel version of the classical Jacobi algorithm for solving a real symmetric eigenvalue problem. This is a “symmetric” problem (due to the periodicity) with infinitely many solutions. Let us now consider an arbitrary non-symmetric “small” perturbation of the above equation. For instance, the equation sin x = 1/2 + εx 2 has finitely many solutions, for any ε ≠ : D. Motreanu, V. Rădulescu.

    The non–symmetric eigenvalue problem We now know how to find the eigenvalues and eigenvectors of any symmetric n ×n matrix, no matter how large. This is useful in the the calculus of several variables since Hessian matrices are always symmetric. Hence we have the means to find the eigenvectors. The same applies to invariant subspaces, which for example can describe sets of initial states for which a dynamical system produces exponentially decaying states. Computing eigenvalues has a long history, dating back to at least when Jacobi [] wrote his Brand: Springer-Verlag Berlin Heidelberg.

    Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem Article (PDF Available) in European Physical Journal Plus (8) January with Reads. Wilkinson's () book provides an excellent compendium on the problem. The eigenvalue problems arising out of finite element models are a particular case: they involve large but usually narrowly banded matrices, and only a small number of eigenpairs are usually required. For many important cases the matrices are symmetric.


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The symmetric eigenvalue problem by Beresford N. Parlett Download PDF EPUB FB2

It is trite but true to say that research on the symmetric eigenvalue problem has flourished since the first edition of this book appeared in I had dreamed of including the significant new material in an expanded The symmetric eigenvalue problem book edition, but my own research obsessions diverted me from reading, digesting, and then regurgitating all that work.

According to Parlett, "Vibrations are everywhere, and so too are The symmetric eigenvalue problem book eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in ).

The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments.

The commentary is lively but the proofs are by: In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly.

The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of Reviews: 1. About this Item: Independently Published, United States, Paperback. Condition: New.

Language: English. Brand new Book. The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it.

Reviews the non-fiction book 'The Symmetric Eigenvalue Problem,' by Beresford N. Parlett. ACCESSION # Related Articles. Eigenvalues in Riemannian Geometry (Book). Berger, Melvin S. // American Scientist;May/Jun87, Vol. 75 Issue 3, p Nandy S, Sharma R and Bhattacharyya S () Solving symmetric eigenvalue problem via genetic algorithms, Applied Soft Computing,(), Online publication date: 1-Jul Aminikhah H and Jamalian A () A new algorithm for computing eigenpairs of matrices, Mathematical and Computer Modelling: An International Journal, The symmetric eigenvalue problem Beresford N.

Parlett A droll explication of techniques that can be applied to understand some of the most important engineering problems: those dealing with vibrations, buckling, and earthquake resistance.

Additional Physical Format: Online version: Parlett, Beresford N. Symmetric eigenvalue problem. Englewood Cliffs, N.J.: Prentice-Hall, © (OCoLC) ISBN: OCLC Number: Description: 1 vol. (xix p.) ; 24 cm. Contents: Basic facts about self-adjoint matrices --Tasks, obstacles, and aids --Counting eigenvalues --Simple vector iterations --Deflation --Useful orthogonal matrices --Tridiagonal form --The QL and QR algorithms --Jacobi methods --Eigenvalue bounds --Approximations from a subspace --Krylov.

Introduction. This chapter takes up the task of computing some, or all, of the pairs (λ, z) such that (A − λ M) z = o, z ≠ o given two symmetric matrices A and M.

The scalar λ is called an eigenvalue (or root) of the pair (A, M) and z is an [Gantmacher, ] the matrix A − λM is called a matrix rather strange use of the word “pencil” comes from.

The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments.

The commentary is lively but the proofs are terse.5/5(2). This chapter discusses sparse eigenanalysis.

The standard eigenvalue problem is defined by Ax = λx, where A is the given n by n matrix. The generalized eigenvalue problem is Ax = λBx where A and B are given n by n matrices and λ and x is wished to be determined.

For. For symmetric tridiagonal eigenvalue problems all eigenvalues (without eigenvectors) can be computed numerically in time O(n log(n)), using bisection on the characteristic polynomial. Iterative algorithms. Iterative algorithms solve the eigenvalue problem by producing sequences that.

The Symmetric Eigenvalue Problem William Ford, in Numerical Linear Algebra with Applications, Symmetric matrices appear naturally in many applications that include the numerical solution to ordinary and partial differential equations, the theory of quadratic forms, rotation of axes, matrix representation of undirected graphs, and.

: The Symmetric Eigenvalue Problem (Classics in Applied Mathematics) () by Parlett, Beresford N. and a great selection of similar 5/5(1). The Interval Eigenvalue Problem. the symmetric case is introduced first with the results generalized later on.

The present book is the first volume of a three : Assem Deif. First published inthis book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book deals with 'symmetric' problems/5.

A Survey of Matrix Inverse Eigenvalue Problems Daniel Boley and Gene H. Golub 0. Introduction. In this paper, we present a survey of some recent results regarding direct methods for solv-ing certain symmetric inverse eigenvalue e eigenvalue problems have been of.

Barucq H, Bekkey C and Djellouli R () Construction of local boundary conditions for an eigenvalue problem using micro-local analysis, Journal of Computational Physics,(), Online publication date: Jan.

Several books dealing with numerical methods for solving eigenvalue prob-lems involving symmetric (or Hermitian) matrices have been written and there are a few software packages both public and commercial available. The book by Parlett [] is an excellent treatise of File Size: 2MB.An Robust Eye Gaze Tracking Eigenvalue Extraction Algorithm Based on 2-D Mapping Model International Conference on Computer Research and Development, 5th (ICCRD ) Stable Analysis on Speed Adaptive Observer in Low Speed OperationCited by: Eigenvalues & Eigenvectors:Eigenvalues & Eigenvectors: 1/3 zGiven a square matrixGiven a square matrix A,ifonecanfinda, if one can find a number (real or complex) λand a vector x such that A⋅x = λxholds, λisaneigenvalueandis an eigenvalue and xan eigenvector corresponding to λ(of matrix A).

zSincetherightSince the right-handsideofhand side of A⋅x=x = λxcanbecan beFile Size: KB.