Analysis of Numerical Methods (Dover Books on Mathematics)

Isaacson & Keller go into great mathematical detail for the several methods; it fills-in the details which are outside of the scope of the many "Numerical Methods in <Programming Language>" books. The authors include a number of good Physics applications and problems, in addition to theorem/proof stuff one would expect in an applied math text designed for an Upper Division Undergraduate or Graduate Level course. The authors are explicit about the assumed prerequisites of Advanced Calculus (multi-variable) and Linear Algebra. A year of calculus-based Physics would help to provide a conceptual application context. (It's kind of funny that nearly EVERY PROBLEM boils down to a problem in Linear Algebra!) The table of contents of the many implementation books follow the sequence of this book, such as "Applied Numerical Methods with MATLAB for Engineers and Scientists" by Chapra. The 1993 and 1966 prefaces identify additional topics which are omitted only for the sake of size of the book, but encourages the reader to explore those topics based on this work. The bibliography identifies much of the seminal work published before 1966; the older works tend to be better-written compared to more contemporary ones.

The book is an excellent overview of the fundamental topics of numerical analysis. It does not cover finite element methods, but goes over most other methods that one should know.

I got the book as a recommended reference for an advanced CFD class. It presents clearly and rigorously (for what I have read) numerical methods that prove to be useful for higher order accuracy CFD schemes (and probably a lot of other fields). I liked it, and I'll keep using it at a reference. Last advantage: it is dirt cheap.

It starts with introductory topics and contexts with which many UG Math students can understand, I believe. It is suitable for most mathematics lover.

Very heavy on analysis. Am sure would appeal to the rigorous guys, but I couldnt get much out of it. I switched to another title by Devorich.

great book w/ lots of helpful info. Surprisingly useful for my needs

This is a classic book on the subject (at a great price) that everyone should have as a reference if they do any type of computational work.

This was my professor's chosen text for my undergrad Numerical Analysis course at UC Berkeley (Math 128A). I would not recommend this text to any undergrad or student who has not had numerical analysis before. The author is much too terse (imitating Rudin, but poorly) and incredibly unclear with explanations. Often gives explanations as "exercises to the reader". (Griffiths does this well, this book does not.) The book also switches notation and indexing haphazardly and without explanation. Simple things like section and equation numbering are woefully neglected and frustrating for the reader. This book was ultimately useless to our class, except as an equation reference, which was also a miserable experience given the careless notation and numbering. Unless you've had numerical analysis before, request a different text from your professor.

Das Buch "Analysis of numerical Methods" von E. Issacson und H.B. Keller erschien 1966 in 1. Auflage 1966 und wurde 1994 aktualisiert. Es enthält eine breite Darstellung der wesentlichen Kapitel eines Numerik-Buchs: Lineare und nichtlineare Gleichungen, Matrizen, Approximation und Interpolation, numerisches Integrieren von Funktionen und gewöhnlichen Differenzialgleichungen. Auffällig ist, dass im Kapitel über Eigenwerte die üblichen Bezeichnungen fehlen: wie der Rayleigh-Ritz-Quotient und die Householder-Spiegelung. Wie das Publikationsdatum zeigt, können neuere Methoden nicht enthalten sein. So fehlen die Algorithmen, die auf dem Krylow-Unterraum-Verfahren beruhen, wie das Arnoldi-Verfahren und andere.