Infinite-Dimensional Spectral Computations: Foundations, Algorithms, and Modern Applications (Cambridge Monographs on Applied and Computational Mathematics)

Colbrook, Matthew J.

ISBN 10: 1009382527 / ISBN 13: 9781009382526

Published by Cambridge University Press, 2026

About this Item

Seller Inventory # I-9781009382526

Bibliographic Details

• Title: Infinite-Dimensional Spectral Computations: Foundations, Algorithms, and Modern Applications (Cambridge Monographs on Applied and Computational Mathematics)
• Publisher: Cambridge University Press
• Publication Date: 2026
• Language: English
• ISBN 10: 1009382527
• ISBN 13: 9781009382526
• Binding: Hardcover
• Condition: New

About this title

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.

About the Author

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.