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Friday, August 7, 2020 | History

5 edition of Computational methods for matrix Eigenproblems found in the catalog.

Computational methods for matrix Eigenproblems

by A. R. Gourlay

  • 30 Want to read
  • 36 Currently reading

Published by Wiley in London, New York .
Written in English

    Subjects:
  • Matrices.,
  • Eigenvalues.,
  • Eigenvectors.

  • Edition Notes

    Bibliography: p. 130.

    Statement[by] A. R. Gourlay [and] G. A. Watson.
    ContributionsWatson, G. A., joint author.
    Classifications
    LC ClassificationsQA193 .G68
    The Physical Object
    Paginationxi, 132 p.
    Number of Pages132
    ID Numbers
    Open LibraryOL5411854M
    ISBN 100471319155
    LC Control Number73002783

    In Chapter 3, iterative projection methods are introduced as they are the major tool for computing extremal eigenvalues of large sparse eigenproblems employing rapidly convergent iterations. Particular examples are the power and Rayleigh-Ritz iterations but also a number of more refined methods are described. This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a .

    A nonlinear eigenproblem is a generalization of an ordinary eigenproblem to equations that depend nonlinearly on the eigenvalue. Specifically, it refers to equations of the form: =,where x is a vector (the nonlinear "eigenvector") and A is a matrix-valued function of the number (the nonlinear "eigenvalue"). (More generally, () could be a linear map, but most commonly it is a . 'This is a truly unique book that covers a variety of computational methods for several important physical (electromagnetics) problems in a rigorous manner with a great depth. It will benefit not only computational mathematicians, but also physicists and electrical engineers interested in numerical analysis of electrostatic, electrodynamic, and Cited by:

      The topics covered range from studies of theoretical aspects of computational methods through to simulations of large-scale industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Implementation of the Lanczos Method for Solving Eigenproblems on the VPP Supercomputer; Matrix Methods. Buy Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) third edition by Golub, Gene H., Van Loan, Charles F. van (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders/5(26).


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Computational methods for matrix Eigenproblems by A. R. Gourlay Download PDF EPUB FB2

Computational methods for matrix Eigenproblems Hardcover – by A. R Gourlay (Author) › Visit Amazon's A. R Gourlay Page. Find all the books, read about the author, and more. See search results for this author. Are you an author. Learn about Author by: Buy Computational Methods for Matrix Eigenproblems on FREE SHIPPING on qualified orders Computational Methods for Matrix Eigenproblems: A.

Gourlay, G. Watson: : Books. Computational methods for matrix Eigenproblems. London, New York, Wiley [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Adrian R Gourlay; G A Watson.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Matrix Methods. Authors; Authors and affiliations A principal factor in attaining high performance is the use of dense matrix computational kernels, which have proved extremely effective in the dense case. (), where references are listed. Saad () has written a book on large-scale eigenproblems with an emphasis on.

Eigenvalue computation in the 20th century. Author links open overlay panel Gene H. Golub 1 a Henk A. van This paper sketches the main research developments in the area of computational methods for eigenvalue problems during the 20th century.

A modern treatment of perturbation theory for a variety of eigenproblems is given in the book Cited by: Computational Methods for Matrix Eigenproblems, John Wiley & Sons, New York.

Introduction. Background Theory. Reductions and Transformations. Methods for the Dominant Eigenvalue. Methods for the Subdominant Eigenvalue. Inverse Iteration.

Jacobi's Methods. Givens and Householder's Methods. Eigensystem of a Symmetric Tridiagonal Matrix. Matrix multiplication problems: Basic algorithms and notations, exploiting structure, block matrices and algorithms, vectorization and re-use issues.

Matrix analysis: basic ideas from linear algebra, vector norms, matrix norms, finite precision matrix computations, orthogonality and SVD, projections and the CS decomposition, the sensitivity of square linear systems.

1) then v is an eigenvector of the linear transformation A and the scale factor λ is the eigenvalue corresponding to that eigenvector. Equation (1) is the eigenvalue equation for the matrix A. Equation (1) can be stated equivalently as (A − λ I) v = 0, {\displaystyle (A-\lambda I)v=0,} (2) where I is the n by n identity matrix and 0 is the zero vector.

Eigenvalues and the characteristic. It is worth mentioning that the complex modes can also be efficiently calculated using the computational methods in the original space (see, e.g., Kwak, ;Tang and Wang, ;Adhikari and.

Functions of Matrices: Theory and Computation - Ebook written by Nicholas J. Higham. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Functions of Matrices: Theory and Computation. Computational Methods for Matrix Eigenproblems: A.R. Gourlay, G. Watson: Books - or: A.R. Gourlay, G. Watson. The results show that the central difference method has high computational efficiency and parallel effectiveness in the case of a diagonal mass and damping matrix and is recommended in such a case.

A comparison is also made between the Cholesky decomposition method and a mixed Jacobi/Gauss–Seidel method when they are incorporated in the. methods and some bad methods, as well as good methods, are presented for pedagogical reasons. Why one method does not work is almost as important as why another method does work.

The material in the book is divided into three main parts: I. Basic tools of Numerical Analysis II. Ordinary Differential Equations III. Partial Differential Size: KB. This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms.

This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to.

Buy a cheap copy of Numerical Linear Algebra book by David Bau III. This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and Free shipping over $/5(5). We give an overview of computational methods for the eigenproblem Ax = λx and related eigenproblems, in particular those for large matrices.

Subspace methods, including the Author: Henk Van Der Vorst. SIAM Journal on Matrix Analysis and ApplicationsAbstract | PDF ( KB) () A global harmonic Arnoldi method for large non-Hermitian eigenproblems with an application to multiple eigenvalue by: The irbleigs code is an implementation of an implicitly restarted block-Lanczos method for computing a few selected nearby eigenvalues and associated eigenvectors of a large, possibly sparse, Hermitian matrix code requires only the evaluation of matrix-vector products with A; in particular, factorization of A is not demanded, nor is the solution of linear systems of Cited by:.

A Brief Survey of Computational Photonics Steven G. Johnson, J. N. Winn, R. D. Meade, and J. D. Joannopoulos Octo Introduction to Book Excerpt The following text is excerpted from the upcoming second edition of the book Photonic Crystals: Molding the Flow of Light (Princeton University Press), sched-uled for publication in spring Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology.

The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and.In this chapter, we describe domain decomposition and block matrix methods for large sparse symmetric eigenproblems [WI8, PA7, CH21, GO4, CI4, SA].

We focus on algorithms which iteratively approximate the minimal eigenvalue and corresponding eigenvector of a matrix, though most such methods can also be extended to simultaneously approximate several eigenvalues.