Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Algebra --- Harmonic analysis. Fourier analysis --- Mathematics --- Fourieranalyse --- algebra --- reeksen (wiskunde) --- functies (wiskunde) --- wiskunde

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Algebra --- algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli of smoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic properties of the classical orthogonal polynomials the book provides new results on nonclassical orthogonal polynomials including methods for their numerical construction.

Algebra --- Harmonic analysis. Fourier analysis --- Mathematics --- Fourieranalyse --- algebra --- reeksen (wiskunde) --- functies (wiskunde) --- wiskunde