Infinite-Dimensional Spectral Computations: Foundations, Algorithms, and Modern Applications - Couverture rigide

Colbrook, Matthew J.

Couverture rigide

ISBN 10 : 1009382527 ISBN 13 : 9781009382526

Editeur : Cambridge University Press, 2026

Synopsis

Mathematicians, physicists, engineers, and data scientists will welcome this comprehensive, rigorous, and practical guide to computing spectral properties of operators in infinite-dimensional settings. It explains why standard discretisation can fail and shows how to overcome these pitfalls. It develops resolvent-based algorithms with provable convergence and certified error bounds, organised by a precise computability classification that clarifies what is achievable, what is impossible, and what extra information makes problems tractable. Topics include spectra and pseudospectra, spectral measures and functional calculus, spectral types, fractal and Cantor-type spectra, essential versus discrete spectra and multiplicities, spectral radii, abscissas and gaps, nonlinear operator pencils, and verified computation. A distinctive feature is the integration of modern applications, including a fully rigorous treatment of data-driven Koopman spectral analysis. Hundreds of worked examples, exercises with solutions, notes, and usable code make the book both a reference and a powerful toolkit for researchers and students.

A propos du livre

À propos de l'auteur

Matthew J. Colbrook is Associate Professor at the University of Cambridge. His research spans analysis, numerical algorithms, and data science, and he is known for his work on operator spectra. His work has been recognized by prizes including the Popov Prize and the SIAM DiPrima Prize.

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 1009382527
• ISBN 13: 9781009382526
• Reliure: Relié
• Nombre de pages: 705
• Coordonnées du fabricant: non disponible
• Personne responsable: Avery; https://www.avery.fr/; ; chemin des peupliers 27; Dardilly; France