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Victor S. Ryaben'kii, Semyon V Tsynkov
... 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
Nonlocal Continuum Limits of p-Laplacian...
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Inverse Problems and Data Assimilation...
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Inverse Problems and Data Assimilation...
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Introduction to Modeling and Numerical...
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