Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals - Couverture souple

Schreiber, Kathrin

 
9783639062519: Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals
Couverture souple
ISBN 10 : 3639062515 ISBN 13 : 9783639062519
Editeur : 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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Présentation de l'éditeur

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.

Biographie de l'auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2008
Langue
anglais
ISBN 10 
3639062515
ISBN 13 
9783639062519
Reliure
Broché
Nombre de pages
208
Coordonnées du fabricant
non disponible
Personne responsable
non disponible