A Brief Introduction to Numerical Analysis - Softcover

Tyrtyshnikov, Eugene E.

Softcover

ISBN 10: 1461264138 ISBN 13: 9781461264132

Publisher: Birkhäuser, 2012

Synopsis

Probably I ought to explain why one more book on numerical methods can be useful. Without any doubt, there are many quite good and excellent books on the subject. But I know definitely that I did not realize this when I was a student. In this book, my first desire was to present those lectures that I wished I would have heard when I was a student. Besides, in spite of the profusion of textbooks, introductory courses, and monographs on numerical methods, some of them are too elementary, some are too difficult, some are far too overwhelmedwith applications, and most of them are too lengthy for those who want to see the whole picture in a short time. I hope that the brevity of the course left me no chance to obscure the beauty and depth of mathematical ideas behind the theory and methods of numerical analysis. I am convincedthat such a book should be very conciseindeed. It should be thoroughly structured, giving information in short sections which, ideally, are a half-page in length. Equally important, the book should not give an impression that nothing is left to work on in this field. Any time it becomes possible to say something about modern development and recent results, I do try to find time and place for this.

About this title

Review

"The title of this book reflects its structure and style with great exactness... The presentation of the material is very clear and supported by properly chosen exercises of good didactic value added to each lecture."

- Zentralblatt Math

"[The book] is a short and elegant coupling of simplicity and very deep results...[It] can be used both as an introduction and a refinement to a university course. Students [in] mathematics and physics but also other advanced readers and experienced researchers find both the classical fundamental results and new visions and ideas while reading this nice book."

- ZAA

From the Back Cover

This is an advanced textbook based on lectures delivered at the Moscow Physico-Technical Institute. Brevity, logical organization of the material, and a sometimes lighthearted approach are distinctive features of this modest book. The author makes the reader an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis in a short time. Since matrix analysis underlies numerical methods and the author is an expert in this field, emphasis in the book is on methods and algorithms of matrix analysis. Also considered are function approximations, methods of solving nonlinear equations and minimization methods. Alongside classical methods, new results and approaches developed over the last few years are discussed - namely those on spectral distribution theory and what it gives for design and proof of modern preconditioning strategies for large-scale linear algebra problems. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful. It can be equally useful for advanced readers and researchers in providing them with new findings and new accessible views of the basic mathematical framework.

Edition details

• Publisher: Birkhäuser
• Publication date: 2012
• Language: English
• ISBN 10: 1461264138
• ISBN 13: 9781461264132
• Binding: Paperback
• Number of pages: 214