Classical Numerical Analysis

Synopsis

Classical Numerical Analysis: A Comprehensive Course (CNA) is our new book (2023) on numerical analysis aimed at graduate and advanced undergraduate students and published by Cambridge University Press. Written by my colleague, Abner Salgado, and myself, CNA is our attempt to make numerical analysis accessible and understandable to a modern audience. The following is the back-cover blurb for the book:

Numerical Analysis is a broad field, and coming to grips with all of it may seem like a daunting task. This text provides a thorough and comprehensive exposition of all the topics contained in a classical graduate sequence in numerical analysis. With an emphasis on theory and connections with linear algebra and analysis, the book shows all the rigor of numerical analysis. Its high level and exhaustive coverage will prepare students for research in the field and become a valuable reference as they continue their career. Students will appreciate the simple notation, clear assumptions and arguments, as well as the many examples and classroom-tested exercises ranging from simple verification to qualifying exam-level problems. In addition to the many examples with hand calculations, readers will also be able to translate theory into practical computational codes by running sample MATLAB codes as they try out new concepts.

Editorial Reviews

• Endre Süli, University of Oxford: ‘This impressive volume covers an unusually broad range of topics in the field of numerical analysis, including numerical linear algebra, polynomial and trigonometric interpolation, best approximation, numerical quadrature, the approximate solution of nonlinear equations and convex optimization, and the numerical solution of ordinary and partial differential equations by finite difference, spectral and finite element methods. A particularly appealing feature of the text is the way in which it integrates a mathematically rigorous exposition with a wealth of illustrative examples, including numerical simulations, sample codes, and exercises. I warmly recommend the book to students and lecturers as an advanced undergraduate or introductory graduate level text.’

• Maxim Olshanskii, University of Houston: ‘This long-awaited graduate text covers every topic of a traditional, one-year Numerical Analysis course in an accessible, rigorous, and comprehensive way. It’s an indispensable assistant for anyone offering the class and a precious source of knowledge for a junior researcher in the field.’

• Arieh Iserles, University of Cambridge: ‘This is the book I have been waiting for: a textbook of numerical analysis fit for the Twenty-First Century. It sketches a path from the mathematical foundations of the subject to the wide range of its modern methods and algorithms, compromising on neither rigour nor clarity.’

• Xiaofan Li, Illinois Institute of Technology: ‘The book is the only textbook I know that covers the current topics for beginning graduate students in numerical analysis. The chosen topics in the book match exactly what one wishes to cover in a two-semester course sequence in computational mathematics, as the selection of the numerical methods is in align with the modern treatment of the subjects. Many instructors in the field have struggled to find two or more textbooks for the same coverage, but you can have all of them in this book.’

Availability

The electronic version of the book can be found on Cambridge Core here. Please (pray hands) ask your university library to purchase campus-wide access to the electronic version from Cambridge Core for you and your students. If you are more of an old-school type, the hardback can be purchased on Amazon (in the United States and Europe) and directly from Cambridge University Press.

Errata

No book that can be written can be written without errors. Our book has a few of them (wink). You can get the errata file from the GitHub repo for the book here. Errors, typos and inconsistencies can be reported to either Abner or me. See my email address below. We greatly appreciate any feadback you have to give about the book.

Codes

There are several Matlab codes that are listed in the book, and these may be retrieved from the GitHub repo: stevenmwise/ClassicalNumericalAnalysis. In addition, you can obtain the Matlab source codes used to generate the tables and figures dispayed in the book. We plan to add more software and supplementary material over time to the repo.

Solutions

We are working on a partial solutions manual, though it may not be ready until 2024/5. If you are an instructor teaching from the book, feel free to inquire about the status of the solutions project. We would be glad to hear from you.