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3 edition of The use of Lanczos"s method to solve the large generalized symmetric definite eigenvalue problem found in the catalog.

The use of Lanczos"s method to solve the large generalized symmetric definite eigenvalue problem

The use of Lanczos"s method to solve the large generalized symmetric definite eigenvalue problem

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  • 18 Currently reading

Published by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va .
Written in English

    Subjects:
  • Algorithms.,
  • Buckling.,
  • Eigenvalues.,
  • Problem solving.,
  • Structural engineering.,
  • Vibration.

  • Edition Notes

    StatementMark T. Jones, Merrell L. Patrick.
    SeriesICASE report -- no. 89-69., NASA contractor report -- 181914., NASA contractor report -- NASA CR-181914.
    ContributionsPatrick, Merrell L., Langley Research Center.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL16121058M

    In the first part of this thesis, methods for the partial solution of generalized eigenvalue problems arising from structural dynamics are studied. A natural choice for partially solving the generalized eigenvalue problem (GEP) is the Lanczos iteration, or the shift-and-invert Lanczos (SIL) algorithm if a large number of eigenpairs is required. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An "industrial strength" algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm.

    First published in , Lanczos Algorithms for Large Symmetric Eigenvalue Computations; Vol. I: Theory 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. We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX −1 L T, where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval.

    Abstract. This work presents an adaptive block Lanczos method for large-scale non-Hermitian Eigenvalue problems (henceforth the ABLE method). The ABLE method is a block version of the non-Hermitian Lanczos algorithm. There are three innovations. Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Theory Vol. I by Jane K. Cullum, , available at Book Depository with free delivery worldwide.


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The use of Lanczos"s method to solve the large generalized symmetric definite eigenvalue problem Download PDF EPUB FB2

The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new. The Use of Lanczos's Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem Mark T.

Jones*and Merrell L. Patrick*t Abstract The generalized eigenvalue problem, Kx = XMx, is of signifi-cant practical importance, especially in structural engineering where it arises as the vibration and buckling problems.

Get this from a library. The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem in parallel. [Mark T Jones; Merrell L Patrick; Institute for Computer Applications in Science and Engineering.].

Get this from a library. The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem. [Mark T Jones; Merrell L Patrick; Langley Research Center.].

The Use of Lanczos's Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem Mark T. Jones*and Merrell L. Patrick *t Abstract The generalized eigenvalue problem, Kx._Mx, is of signifi- cant practical importance, especially in structural engineering where it arises as the vibration and buckling problems.

The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems By Thomas Ericsson and Axel Ruhe Abstract. A new algorithm is developed which computes a specified number of eigen-values in any part of the spectrum of a generalized symmetric matrix eigenvalue prob-lem.

This paper describes a restarted Lanczos algorithm that particularly suitable for implementation on distributed machines. The only communication operation is requires outside of the matrix-vector. A new algorithm is developed which computes a specified number of eigenvalues in any part of the spectrum of a generalized symmetric matrix eigenvalue problem.

It uses a linear system routine (factorization and solution) as a tool for applying the Lanczos algorithm to a shifted and inverted problem. The algorithm determines a sequence of shifts and checks that all eigenvalues get.

Lanczos method solves the approximate problem: (). Findxm e x0 A Km such that Pm(b - Axm) = 0. In exact arithmetic, the approximation xm thus computed is identical with that provided by m steps of the conjugate gradient (CG) method when A is positive definite [9].

The original Lanczos algorithm was developed for handling the standard eigenvalue problem only, i.e., B = I. Extensions to the generalized eigenvalue problem [11], [21], [16] require solving a linear system of the form Bx = b at each iteration step, or factorizing matrices of the form A − σB during the iteration.

2 THE ADAPTED LANCZOS ALGORITHM The generalized linear eigenvalue buckling problem is ù Ö L ã ù õ Ö 1 where K is the stiffness matrix, is the eigenvector, λ is the eigenvalue and KG is the geometric stiffness matrix.

K is symmetric and positive‐definite. KG is symmetric but may not be positive‐definite. In classical linearized buckling. The spectral transformation Lanczos method is very popular for solving large scale real symmetric generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used.

Sometimes, a semi-definite inner product must be used. This may lead to instabilities and break-down. 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' : Paperback. An interative reduction of the matrix size is attained by the biorthogonal Lanczos algorithm which allows extraction of the lower eigenvalue spectrum. In this paper, we present a new restarting method in the Lanczos algorithm for computing a few eigenvalues of the symmetric positive definite eigenvalue problem, AX = λBX, where A and B are large and sparse matrices.

The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy. Lanczos algorithm is a very effective method for finding extreme eigenvalues of symmetric matrices. It requires less arithmetic operations than similar algorithms, such as, the Arnoldi method.

In this paper, we present our parallel version of the Lanczos method for. The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem.

A new algorithm, LANZ, based on Lanczos's method is developed. Mitsuhiro KASHIWAGI, A METHOD FOR DETERMINING EIGENSOLUTIONS OF LARGE, SPARSE, SYMMETRIC MATRICES BY THE PRECONDITIONED CONJUGATE GRADIENT METHOD IN THE GENERALIZED EIGENVALUE PROBLEM, Journal of Structural and Construction Engineering (Transactions of AIJ), 73,(), ().

the standard Lanczos algorithm is extended to solve the symmetric generalized eigenvalue problem Ax = ABx. Today, the Lanczos algorithm is regarded as the most powerful tool for finding a few eigenvalues of a large symmetric eigen- value problem.

Software, developed by. A parallel Lanczos method for symmetric generalized eigenvalue problems. () New Methods for Calculations of the Lowest Eigenvalues of the Real Symmetric Generalized Eigenvalue Problem. Journal of Computational Physics() Jacobi—Davidson algorithm and its application to modeling RF/Microwave detection circuits.Abstract The Lanczos algorithm was originally used to tridiagonalize symmetric matrices, but it was soon replaced by more effective methods based on explicit orthogonal similarity transformations.

The algorithm was later revived as an effective scheme for solving sparse symmetric eigenvalue problems. An “industrial strength” algorithm for solving sparse symmetric generalized eigenproblems is described.

The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm.