A Brief Introduction to Numerical Analysis - Hardcover

Tyrtyshnikov, Eugene E.

Hardcover

ISBN 10: 0817639160 ISBN 13: 9780817639167

Publisher: Birkhauser Boston Inc, 1997

Synopsis

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 compact book. The author turns the reader into an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis. 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 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, providing them with new findings and new accessible views of the basic mathematical framework.

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 resultsa ][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

Synopsis

This is an advanced textbook based on lectures given at the Moscow Physico-Technical Institute. The lectures are characterized by brevity, logical organization, and occasionally a lighthearted approach. It aims to involve the reader by asking questions, hinting, giving recommendations, comparing different methods, and discussing "optomistic" and "pessemistic" approaches to numerical analysis. Since matrix analysis underlies numerical analysis, this text emphasizes methods and algorithms of matrix analysis. Function approximations, methods of solving nonlinear equations, and minimization methods are also considered. As well as considering classical methods, new methods and approaches are discussed - such as spectral distribution theory and what it offers for design and proof of modern preconditioning strategies for large-scale linear algebra problems.

Edition details

• Publisher: Birkhauser Boston Inc
• Publication date: 1997
• ISBN 10: 0817639160
• ISBN 13: 9780817639167
• Binding: Hardcover
• Language: English
• Number of pages: 205