Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals - Softcover

Schreiber, Kathrin

 
9783639062519: Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals
Softcover
ISBN 10: 3639062515 ISBN 13: 9783639062519
Publisher: VDM Verlag Dr. Müller, 2008

Synopsis

Nonlinear eigenvalue problems arise in many fields of natural and engineering sciences. Theoretical and practical results are scattered in the literature and in most cases they have been developed for a certain type of problem. In this book we consider the most general nonlinear eigenvalue problem without assumptions on the structure or spectrum and provide basic facts.Nonlinear Rayleigh functionals are analyzed in detail and in different forms. New methods for the computation of eigenvalues and -vectors are designed based on Rayleigh functionals, and well-known Jacobi--Davidson methods are discussed. Asymptotically cubic convergence of the two-sided nonlinear Jacobi--Davidson method is shown.The special case of nonlinear complex symmetric eigenvalue problems is examined. We show the appropriate definition of a complex symmetricRayleigh functional, which is used to derive a complex symmetric Rayleigh functionaliteration which converges locally cubically, and the complex symmetric residual inverse iteration method. All methods are also illustrated numerically.The book is addressed to mathematicians as well as engineers interested in nonlinear eigenvalue problems.

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About the Author

Kathrin Schreiber, Dipl.-Math., studied Mathematics in Dresden and Glasgow, completed her Ph.D. at Technische Universität Berlin in 2008.

"About this title" may belong to another edition of this title.

Publisher
VDM Verlag Dr. Müller
Publication date
2008
Language
English
ISBN 10 
3639062515
ISBN 13 
9783639062519
Binding
Paperback
Number of pages
208