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A Theoretical Introduction to Numerical Analysis Synopsis

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. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon's potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

Book Information

ISBN: 9781584886075
Publication date: 2nd November 2006
Author: Victor S. (Keldysh Institute for Applied Math, Moscow, Russia) Ryaben'kii, Semyon V. (North Carolina State University, Tsynkov
Publisher: Chapman & Hall/CRC an imprint of Taylor & Francis Inc
Format: Hardback
Pagination: 552 pages
Categories: Numerical analysis,

About Victor S. (Keldysh Institute for Applied Math, Moscow, Russia) Ryaben'kii, Semyon V. (North Carolina State University, Tsynkov

More About Victor S. (Keldysh Institute for Applied Math, Moscow, Russia) Ryaben'kii, Semyon V. (North Carolina State University, Tsynkov

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