A Theoretical Introduction To Numerical Analysis
by Victor S. Ryaben'kii /
2006 / English / PDF
8.7 MB Download
A Theoretical Introduction to Numerical Analysis
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.
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.
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,
By lucidly presenting the central mathematical concepts of
numerical methods,A Theoretical Introduction to Numerical
Analysis
A Theoretical Introduction to Numerical
Analysis provides a foundational link to more specialized
computational work in fluid dynamics, acoustics, and
electromagnetism.
provides a foundational link to more specialized
computational work in fluid dynamics, acoustics, and
electromagnetism.