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A Theoretical Introduction to Numerical Analysis
ISBN-13:
9781000738285
Veröffentl:
2006
Seiten:
552
Autor:
Victor S. Ryaben’kii
eBook Typ:
EPUB
eBook Format:
EPUB
Kopierschutz:
0 - No protection
Sprache:
Englisch
Beschreibung:
An accessible yet rigorous mathematical introduction, A Theoretical Introduction to Numerical Analysis provides a pedagogical account of the fundamentals of numerical analysis. Using numerical methods from real analysis, linear algebra, and differential equations, the authors explain basic concepts, such as error, discretization, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the smoothness of approximated functions in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation.
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.
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