A Software Repository For Gaussian Quadratures And Christoffel Functions
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A Software Repository For Gaussian Quadratures And Christoffel Functions
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Author : Walter Gautschi
language : en
Publisher: SIAM
Release Date : 2020-10-30
A Software Repository For Gaussian Quadratures And Christoffel Functions written by Walter Gautschi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
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
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Author : Kyle Novak
language : en
Publisher: Equal Share Press
Release Date : 2022-03-13
Numerical Methods For Scientific Computing written by Kyle Novak and has been published by Equal Share Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-13 with Mathematics categories.
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.
A Software Repository For Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: SIAM
Release Date : 2018
A Software Repository For Orthogonal Polynomials written by Walter Gautschi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Science categories.
A Software Repository for Orthogonal Polynomials is the first book that provides graphs and references to online datasets that enable the generation of a large number of orthogonal polynomials with classical, quasi-classical, and nonclassical weight functions. Useful numerical tables are also included. The book will be of interest to scientists, engineers, applied mathematicians, and statisticians.
Theory And Applications Of Gaussian Quadrature Methods
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Author : Narayan Kovvali
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2011-10-10
Theory And Applications Of Gaussian Quadrature Methods written by Narayan Kovvali and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-10 with Technology & Engineering categories.
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. Table of Contents: Introduction / Approximating with Polynomials and Related Functions / Gaussian Quadrature / Applications / Links to Mathematical Software
Calculation Of Special Functions
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Author : C. G. van der Laan
language : en
Publisher:
Release Date : 1984
Calculation Of Special Functions written by C. G. van der Laan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Error functions categories.
Petsc For Partial Differential Equations Numerical Solutions In C And Python
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Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22
Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Creators Of Mathematical And Computational Sciences
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Author : Ravi P Agarwal
language : en
Publisher: Springer
Release Date : 2014-11-11
Creators Of Mathematical And Computational Sciences written by Ravi P Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.
The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.
Introduction To Uncertainty Quantification
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Author : T.J. Sullivan
language : en
Publisher: Springer
Release Date : 2015-12-14
Introduction To Uncertainty Quantification written by T.J. Sullivan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-14 with Mathematics categories.
This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.
Power Line Communications
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Author : Hendrik C. Ferreira
language : en
Publisher: John Wiley & Sons
Release Date : 2011-07-22
Power Line Communications written by Hendrik C. Ferreira and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-22 with Technology & Engineering categories.
Power Line Communications (PLC) is a promising emerging technology, which has attracted much attention due to the wide availability of power distribution lines. This book provides a thorough introduction to the use of power lines for communication purposes, ranging from channel characterization, communications on the physical layer and electromagnetic interference, through to protocols, networks, standards and up to systems and implementations. With contributions from many of the most prominent international PLC experts from academia and industry, Power Line Communications brings together a wealth of information on PLC specific topics that provide the reader with a broad coverage of the major developments within the field. Acts as a single source reference guide to PLC collating information that is widely dispersed in current literature, such as in research papers and standards. Covers both the state of the art, and ongoing research topics. Considers future developments and deployments of PLC
Orthogonal Polynomials In Matlab
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Author : Walter Gautschi
language : en
Publisher: SIAM
Release Date : 2016-05-23
Orthogonal Polynomials In Matlab written by Walter Gautschi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-23 with Science categories.
Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years.?Orthogonal Polynomials in MATLAB: Exercises and Solutions?describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.?