A Software Repository For Gaussian Quadratures And Christoffel Functions

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A Software Repository for Gaussian Quadratures and Christoffel Functions

Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611976359
Total Pages : 152 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis A Software Repository for Gaussian Quadratures and Christoffel Functions by : Walter Gautschi

Download or read book A Software Repository for Gaussian Quadratures and Christoffel Functions written by Walter Gautschi and published by SIAM. This book was released on 2020-10-30 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Kyle Novak
Publisher : Equal Share Press
ISBN 13 :
Total Pages : 710 pages
Book Rating : 4.9/5 (854 download)

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Book Synopsis Numerical Methods for Scientific Computing by : Kyle Novak

Download or read book Numerical Methods for Scientific Computing written by Kyle Novak and published by Equal Share Press. This book was released on 2022-03-13 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Author : Ed Bueler
Publisher : SIAM
ISBN 13 : 1611976316
Total Pages : 407 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis PETSc for Partial Differential Equations: Numerical Solutions in C and Python by : Ed Bueler

Download or read book PETSc for Partial Differential Equations: Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Ravi P Agarwal
Publisher : Springer
ISBN 13 : 3319108700
Total Pages : 514 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Creators of Mathematical and Computational Sciences by : Ravi P Agarwal

Download or read book Creators of Mathematical and Computational Sciences written by Ravi P Agarwal and published by Springer. This book was released on 2014-11-11 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : T.J. Sullivan
Publisher : Springer
ISBN 13 : 3319233955
Total Pages : 351 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Introduction to Uncertainty Quantification by : T.J. Sullivan

Download or read book Introduction to Uncertainty Quantification written by T.J. Sullivan and published by Springer. This book was released on 2015-12-14 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Integration

Author : Terje O. Espelid
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Numerical Integration by : Terje O. Espelid

Download or read book Numerical Integration written by Terje O. Espelid and published by Springer Science & Business Media. This book was released on 1992 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks.

Orthogonal Polynomials

Author : Walter Gautschi
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198506720
Total Pages : 301 pages
Book Rating : 4.5/5 (67 download)

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Book Synopsis Orthogonal Polynomials by : Walter Gautschi

Download or read book Orthogonal Polynomials written by Walter Gautschi and published by Oxford University Press on Demand. This book was released on 2004 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

Orthogonal Polynomials in MATLAB

Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611974305
Total Pages : 345 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Orthogonal Polynomials in MATLAB by : Walter Gautschi

Download or read book Orthogonal Polynomials in MATLAB written by Walter Gautschi and published by SIAM. This book was released on 2016-05-23 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.?

A Software Repository for Orthogonal Polynomials

Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611975220
Total Pages : 67 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis A Software Repository for Orthogonal Polynomials by : Walter Gautschi

Download or read book A Software Repository for Orthogonal Polynomials written by Walter Gautschi and published by SIAM. This book was released on 2018-03-20 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.????

Computer Solution of Linear Algebraic Systems

Author : George Elmer Forsythe
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computer Solution of Linear Algebraic Systems by : George Elmer Forsythe

Download or read book Computer Solution of Linear Algebraic Systems written by George Elmer Forsythe and published by . This book was released on 1967 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The SIAM 100-Digit Challenge

Author : Folkmar Bornemann
Publisher : SIAM
ISBN 13 : 089871561X
Total Pages : 310 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis The SIAM 100-Digit Challenge by : Folkmar Bornemann

Download or read book The SIAM 100-Digit Challenge written by Folkmar Bornemann and published by SIAM. This book was released on 2004-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives concrete examples of how to justify the validity of every single digit of a numerical answer.

Approximation and Computation

Author : Walter Gautschi
Publisher : Springer
ISBN 13 : 9781441965936
Total Pages : 0 pages
Book Rating : 4.9/5 (659 download)

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Book Synopsis Approximation and Computation by : Walter Gautschi

Download or read book Approximation and Computation written by Walter Gautschi and published by Springer. This book was released on 2010-10-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.

Orthogonal Polynomials and Special Functions

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Francisco Marcellàn

Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellàn and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

CUDA for Engineers

Author : Duane Storti
Publisher : Addison-Wesley Professional
ISBN 13 : 013417755X
Total Pages : 739 pages
Book Rating : 4.1/5 (341 download)

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Book Synopsis CUDA for Engineers by : Duane Storti

Download or read book CUDA for Engineers written by Duane Storti and published by Addison-Wesley Professional. This book was released on 2015-11-02 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: CUDA for Engineers gives you direct, hands-on engagement with personal, high-performance parallel computing, enabling you to do computations on a gaming-level PC that would have required a supercomputer just a few years ago. The authors introduce the essentials of CUDA C programming clearly and concisely, quickly guiding you from running sample programs to building your own code. Throughout, you’ll learn from complete examples you can build, run, and modify, complemented by additional projects that deepen your understanding. All projects are fully developed, with detailed building instructions for all major platforms. Ideal for any scientist, engineer, or student with at least introductory programming experience, this guide assumes no specialized background in GPU-based or parallel computing. In an appendix, the authors also present a refresher on C programming for those who need it. Coverage includes Preparing your computer to run CUDA programs Understanding CUDA’s parallelism model and C extensions Transferring data between CPU and GPU Managing timing, profiling, error handling, and debugging Creating 2D grids Interoperating with OpenGL to provide real-time user interactivity Performing basic simulations with differential equations Using stencils to manage related computations across threads Exploiting CUDA’s shared memory capability to enhance performance Interacting with 3D data: slicing, volume rendering, and ray casting Using CUDA libraries Finding more CUDA resources and code Realistic example applications include Visualizing functions in 2D and 3D Solving differential equations while changing initial or boundary conditions Viewing/processing images or image stacks Computing inner products and centroids Solving systems of linear algebraic equations Monte-Carlo computations

Partition of Unity Methods

Author : St¿phane Bordas
Publisher : John Wiley & Sons
ISBN 13 : 0470667087
Total Pages : 373 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis Partition of Unity Methods by : St¿phane Bordas

Download or read book Partition of Unity Methods written by St¿phane Bordas and published by John Wiley & Sons. This book was released on 2023-10-16 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.

Introduction to Numerical Analysis

Author : J. Stoer
Publisher : Springer Science & Business Media
ISBN 13 : 1475722729
Total Pages : 674 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Numerical Analysis by : J. Stoer

Download or read book Introduction to Numerical Analysis written by J. Stoer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Interpolation Processes

Author : Giuseppe Mastroianni
Publisher : Springer Science & Business Media
ISBN 13 : 3540683496
Total Pages : 452 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Interpolation Processes by : Giuseppe Mastroianni

Download or read book Interpolation Processes written by Giuseppe Mastroianni and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (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. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.