The Algebraic Eigenvalue Problem (Numerical Mathematics and Scientific Computation) by the late J. H. Wilkinson (PDF)

Description

This volume, which became a classic on first publication, is perhaps the most important and widely read book in the field of numerical analysis. It presents a distillation of the author’s pioneering discoveries concerning the computation of matrix eigenvalues. The emphasis is on the transmission of knowledge rather than elaborate proofs. The book will be valued by all practicing numerical analysts, students and researchers in the field, engineers, and scientists.

User’s Reviews

Editorial Reviews: Review ” . . . a classic . . . Questions of sensitivity, and the economy and stability of many numerical methods are treated in rigorous detail, but always in a manner accessible to engineers and scientists.” –Quarterly of Applied Mathematics

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The service was prompt because I received the book on the 2nd October 2019. I am proving the existence of a complex zero of a real coefficient twentieth degree polynomial in a disc centered at 3/2 with radius 1/2. I do this by invoking a theorem in complex analytic function theory which requires the validation of an inequality. In order to prove the inequality, I use the material in chapter five to estimate the eigenvalues and eigenvectors of an n x n symmetric matrix.

⭐This is lovingly referred to by numerical analysts as The Old Testament. The newer book – Rounding Errors in Algebraic Processes – is, of course, The New Testament. Together they make up the bible for efficient numerical computation in the digital world. That world is discrete, not continuous so iterative approximation is the order of the day. If your going to approximate, you need to understand, plan for, and minimize your errors. This book is about all of that and more. It’s for professionals who want to do it right. Very thorough and complete.

⭐This book is really something else.I found it in my boss’ collection, and my appreciation to his taste of books doubled instantly as I started going over the pages. I was aware of the book through Golub and Van Loan’s endless citations to it (as AEP) whenever they reach a hard to prove theorem on eigenvalues.Wilkinson presents hardcore material with clarity, I really appreciate the authorship. For those who share my background (electrical engineering), the authorship is similar to Gallager’s “Information Theory and Reliable Communication”, or Wozencraft’s “Principles of Communication Engineering”.Wilkinson is surprising in this book however. Immediately, after hardcore numerical stability bound derivations, he starts giving practical examples, does not appear to talk down to the reader.This book is a treasure. Wilkinson is my hero!Very likely, the book by Parlett “Symmetric Eigenvalue Problem” will be a good companion. When someone borrows your AEP, you can continue learning from SEP.

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