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Numerical analysis --- Numerical analysis.

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Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

Numerical analysis --- Numerical analysis.

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Numerical analysis --- Numerical analysis.

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The wavelet transform has emerged as one of the most promising function transforms with great potential in applications during the last four decades. The present monograph is an outcome of the recent researches by the author and his co-workers, most of which are not available in a book form. Nevertheless, it also contains the results of many other celebrated workers of the ?eld. The aim of the book is to enrich the theory of the wavelet transform and to provide new directions for further research in theory and applications of the wavelet transform. The book does not contain any sophisticated Mathematics. It is intended for graduate students of Mathematics, Physics and Engineering sciences, as well as interested researchers from other ?elds. The Fourier transform has wide applications in Pure and Applied Mathematics, Physics and Engineering sciences; but sometimes one has to make compromise with the results obtainedbytheFouriertransformwiththephysicalintuitions. ThereasonisthattheFourier transform does not re?ect the evolution over time of the (physical) spectrum and thus it contains no local information. The continuous wavelet transform (W f)(b,a), involving ? wavelet ?, translation parameterb and dilation parametera, overcomes these drawbacks of the Fourier transform by representing signals (time dependent functions) in the phase space (time/frequency) plane with a local frequency resolution. The Fourier transform is p n restricted to the domain L (R ) with 1 p 2, whereas the wavelet transform can be de?ned for 1 p.

Numerical analysis. --- Numerical Analysis.

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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.

Numerical analysis --- Numerical analysis.