A Software Repository For Gaussian Quadratures And Christoffel Functions
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A Software Repository for Gaussian Quadratures and Christoffel Functions
This companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions. The repository contains 60+ datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials. Scientists, engineers, applied mathematicians, and statisticians will find the book of interest.
Numerical Methods for Scientific Computing
A comprehensive guide to the theory, intuition, and application of numerical methods in linear algebra, analysis, and differential equations. With extensive commentary and code for three essential scientific computing languages: Julia, Python, and Matlab.
Analysis, Approximation, Optimization: Computation and Applications
This contributed volume is dedicated to Academician Gradimir V. Milovanović on his 75th birthday and contains recent results in the fields of approximation theory, numerical analysis, mathematical analysis, optimization theory, and various applications of an interdisciplinary character. Most of these results were presented in person during an International Conference “Analysis, Approximations and Applications" (AAA2023), organized by the Faculty of Science, University of Kragujevac in Vrnjačka Banja, Serbia (June 21-24, 2023). This book is intended for researchers and students of mathematics and other computational and applied sciences. This book provides surveys of state of the art results in the fields of Extremal Problems, Optimization and Calculus of Variations; Orthogonal Systems and Quadrature Formulas; Differential and Integral Equations, Integral Transforms and Operation Calculus; Analytic Number Theory and Special Functions; Real and Complex Functions, Sequences, Series, Approximations and Expansions; Functional Analysis, Operator Theory, Fixed Point Theory and Iterative Processes, as well as in Miscellaneous Applications.