7 edition of **Large scale eigenvalue problems** found in the catalog.

- 264 Want to read
- 10 Currently reading

Published
**1986**
by North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co. in Amsterdam, New York, New York, N.Y., U.S.A
.

Written in English

- Eigenvalues -- Congresses.,
- Eigenvalues -- Data processing -- Congresses.

**Edition Notes**

Includes bibliographies and index.

Statement | edited by Jane Cullum and Ralph A. Willoughby. |

Series | North-Holland mathematics studies ;, 127 |

Contributions | Cullum, Jane K., 1938-, Willoughby, Ralph A. |

Classifications | |
---|---|

LC Classifications | QA193 .I26 1985 |

The Physical Object | |

Pagination | viii, 330 p. : |

Number of Pages | 330 |

ID Numbers | |

Open Library | OL2720149M |

ISBN 10 | 0444700749 |

LC Control Number | 86013544 |

In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is . problem to a generalized eigenvalue problem. The resulting algorithm is not only robust, due to existing highly advanced eigenvalue solvers, but also provides a new way of employing second order methods in the large scale case. Key words: Cubic Regularization, Generalized Eigenvalue Problem, Large Scale 1 .

The power method for finding the eigenvalue of largest magnitude and a corresponding eigenvector of a matrix is roughly. Pick a random vector ≠.; For ⩾ (until the direction of has converged) do. Let + ′.; Let + = + ′ / ‖ + ′ ‖.; In the large limit, approaches the normed eigenvector corresponding to the largest magnitude eigenvalue.; A critique that can be raised against this. In particular, we quantitatively show that topology-aware mapping of computational tasks to physical processors on large-scale multi-core clusters may have a significant impact on efficiency. For typical large-scale eigenvalue calculations, we obtain up to a factor of improvement in overall performance by using a topology-aware mapping.

Large Scale Eigenvalue Problems: Workshop Proceedings (Mathematics Studies). Elsevier Science Ltd. Used - Good. Former Library book. Shows some signs of . Large scale eigenvalue problems, Lecture 2, Febru 19/ Numerical Methods for Solving Large Scale Eigenvalue Problems Basics The real Schur decomposition The real Schur decomposition *Real matrices can have complex eigenvalues. If complex eigenvalues exist.

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Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems.

The material is accessible for the first time to experts as well as many nonexpert users who need to choose the best. Purchase Large Scale Eigenvalue Problems, Volume - 1st Edition.

Print Book & E-Book. ISBNBook Edition: 1. by the second class of problems. 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 the problem. Despite a rather strongFile Size: 2MB. Search in this book series.

Large Scale Eigenvalue Problems Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems July • Oberlech, Austria.

Edited by Jane Cullum, Ralph A. Willoughby. VolumePages iii-v, (). Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems.

This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need.

Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide. A guide to the numerical solution of eigenvalue problems. This book attempts to present the many available methods in an organized fashion, to make it easier for reader to identify the most promising methods.

Introduction Algorithms for Linear Problems Methods for Nonlinear Eigenvalue Problems Overview 1 Introduction 2 Algorithms for Linear Problems 3 Methods for Nonlinear Eigenvalue Problems Max Planck Institute Magdeburg Patrick Kurschner, Modern Numerical Methods for Large{Scale Eigenvalue Problems.

8 Eigenvalue software 9 Conclusions and acknowledgements References 1. Introduction The algebraic eigenvalue problem Ax = x is fundamental to scienti c computing.

Large-scale problems are of increas-ing importance, and recent advances in the area of nonsymmetric problems have enormously expanded capabilities in areas such as linear. For the small and medium-sized GEP, we can use the QZ algorithm to compute its eigenpairs. For the large-scale GEP, we can apply Krylov subspace methods (see, e.g.,) to find its smallest eigenvalue in we can see that the pole σ is kept unchanged in Algorithmbut we can update the pole σ by using the second newest eigenvalue to improve the computational.

Matrix Eigenvalue Problem is Nonlinear I Large-scale eigenvalue problem Ax = x or Ax = Bx I A, B large, sparse, or structured theory, see Parlett’s book) 0 5 10 15 20 25 30 0 5 10 15 20 Lanczos iteration number Ritz values.

Computation Cost and Acceleration Methods Cost. Large-scale eigenvalue problems Yuxin Chen Princeton University, Fall Outline •Power method •Lanczos algorithm Eigenvalue problems Eigendecomposition.

large eigenvalue problems in practice. In the following, we restrict ourselves to problems from physics [7, 18, 14] and computer science. What makes eigenvalues interesting. In physics, eigenvalues are usually related to vibrations. Objects like violin strings, drums, bridges, sky scrapers can swing.

They do this at certain frequencies. QR technique that is suitable for large-scale problems. Implicit restarting provides a means to approximate a few eigenvalues with user specified properties in space proportional to nk, where k is the number of eigenvalues sought, and n is the problem size.

Generalized eigenvalue problems are discussed in some detail. They arise naturally in. This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices.

It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications.

Numerical Methods for Large Eigenvalue Problems by Yousef Saad. Publisher: SIAM ISBN/ASIN: ISBN Number of pages: Description: This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. • large-scale SVD methods • polynomial eigenvalue problems.

Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of according to MathSciNet, the book has 5/5(1).

Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Lehoucq, D. Sorensen, C. Yang. 8 Oct ARPACK SOFTWARE. ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.

The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise.

This book is a guide to understanding and using the software package ARPACK to solve large algebraic eigenvalue problems.

The software described is based on the implicitly restarted Arnoldi method, which has been heralded as one of the three most important advances in large scale eigenanalysis in the past ten years.

The book explains the acquisition, installation, capabilities, and detailed. An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations.Spectra.

Spectra stands for Sparse Eigenvalue Computation Toolkit as a Redesigned is a C++ library for large scale eigenvalue problems, built on top of Eigen, an open source linear algebra library.

Spectra is implemented as a header-only C++ library, whose .The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.