Spectral Methods For Non Standard Eigenvalue Problems

Author : Călin-Ioan Gheorghiu
Publisher : Springer Science & Business
ISBN 13 : 3319062301
Total Pages : 130 pages
Book Rating : 4.03/5 ( download)

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Download or read book Spectral Methods for Non-Standard Eigenvalue Problems written by Călin-Ioan Gheorghiu and published by Springer Science & Business. This book was released on 2014-04-22 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.

Author : Ravindran Kannan
Publisher : Now Publishers Inc
ISBN 13 : 1601982747
Total Pages : 153 pages
Book Rating : 4.42/5 ( download)

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Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 9781611970739
Total Pages : 292 pages
Book Rating : 4.33/5 ( download)

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Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Author : John P. Boyd
Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.35/5 ( download)

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Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Author : Lloyd N. Trefethen
Publisher : SIAM
ISBN 13 : 0898714656
Total Pages : 179 pages
Book Rating : 4.54/5 ( download)

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Download or read book Spectral Methods in MATLAB written by Lloyd N. Trefethen and published by SIAM. This book was released on 2000-07-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Author : Valentin Lychagin
Publisher : MDPI
ISBN 13 : 303651046X
Total Pages : 204 pages
Book Rating : 4.60/5 ( download)

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Download or read book Geometric Analysis of Nonlinear Partial Differential Equations written by Valentin Lychagin and published by MDPI. This book was released on 2021-09-03 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.

Author : Jie Shen
Publisher :
ISBN 13 : 9787030177223
Total Pages : 224 pages
Book Rating : 4.23/5 ( download)

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Download or read book Spectral and High-order Methods with Applications written by Jie Shen and published by . This book was released on 2006 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 中国科学院科学出版基金资助出版。

Author : Daniel Kressner
Publisher : Springer Science & Business Media
ISBN 13 : 3540285024
Total Pages : 272 pages
Book Rating : 4.21/5 ( download)

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Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.

Author : Marios Charalambides
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.34/5 ( download)

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Download or read book Stable Spectral Methods with No Spurious Eigenvalues written by Marios Charalambides and published by . This book was released on 2005 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Zhaojun Bai
Publisher : SIAM
ISBN 13 : 0898714710
Total Pages : 430 pages
Book Rating : 4.15/5 ( download)

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Download or read book Templates for the Solution of Algebraic Eigenvalue Problems written by Zhaojun Bai and published by SIAM. This book was released on 2000-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.