A Theoretical Introduction to Numerical Analysis

by Victor S. Ryaben'kii, Semyon V. Tsynkov

Overview

A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study.

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Product Details

ISBN-13:	9781000738285
Publisher:	CRC Press
Publication date:	11/02/2006
Sold by:	Barnes & Noble
Format:	eBook
Pages:	552
File size:	5 MB

About the Author

Victor S. Ryaben'kii, Semyon V Tsynkov

Table of Contents

Introduction. Interpolation of Functions. Quadratures. Systems of Scalar Equations. The Method of Finite Differences for the Numerical Solution of Differential Equations. The Methods of Boundary Equations for the Numerical Solution of Boundary Value Problems. References. Index.

Editorial Reviews

… presents the general methodology and principles of numerical analysis, illustrating the key concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on hoe to efficiently represent mathematical models for computer-based study. … this book provides a pedagogical account of the fundamentals of numerical analysis. … provides a foundation link to more specialized computational work in mathematics, science, and engineering. … Discusses three common numerical areas: interpolation and quadratures, linear and nonlinear solvers, and finite differences. Explains the most fundamental and universal concepts, including error, efficiency, complexity, stability, and convergence. Addresses advance topics, such as intrinsic accuracy limits, saturation of numerical methods by smoothness, and the method of difference potentials. Provides rigorous proofs for all important mathematical results. Includes numerous examples and exercises to illustrate key theoretical ideas and to enable independent study. ”
— In Mathematical Reviews, Issue 2007g

“It is an excellent book, having a wide spectrum of classical and advanced topics. The book has all the advantages of the Russian viewpoint as well as the Western one.”
—David Gottlieb, Brown University, Providence, Rhode Island, USA

From the Publisher