Approximation of Functions Theory And Numerical Methods

Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided.

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018.

This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods.

by Razvan A. Mezei (Author)

by Santanu Saha Ray (Author), Prakash Kumar Sahu (Author)
This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency

Authors: Römisch, Werner, Zeugmann, Thomas
Many interdisciplinary applications, including support vector machines, kernel-based learning methods, pattern recognition, statistical learning theory, computer graphics, and approximation theory
Rich field experienced enormous development in recent decades, comprising numerical analysis and computational discrete mathematics
Book content tested in lectures, seminars, and discussions at Humboldt University and other institutions over decades

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.