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Author : Aleksandr Semenovich Kronrod
Publisher :
ISBN 13 :
Total Pages : 143 pages
Book Rating : 4.:/5 (73 download)
Download or read book Nodes and Weights of Quadrature Formulas written by Aleksandr Semenovich Kronrod and published by . This book was released on 1965 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Aleksandr S. Konrod
Publisher : Springer
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.F/5 ( download)
Download or read book Nodes and Weights of Quadrature Formulas written by Aleksandr S. Konrod and published by Springer. This book was released on 1965-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Narayan Kovvali
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1608457532
Total Pages : 65 pages
Book Rating : 4.6/5 (84 download)
Download or read book Theory and Applications of Gaussian Quadrature Methods written by Narayan Kovvali and published by Morgan & Claypool Publishers. This book was released on 2011 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Paul F. Byrd
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (31 download)
Download or read book Gauss Quadrature Rules Involving Some Nonclassical Weight Functions written by Paul F. Byrd and published by . This book was released on 1970 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ben Lambert
Publisher : SAGE
ISBN 13 : 1526418266
Total Pages : 744 pages
Book Rating : 4.5/5 (264 download)
Download or read book A Student’s Guide to Bayesian Statistics written by Ben Lambert and published by SAGE. This book was released on 2018-04-20 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes′ rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.
Author : Aldo Ghizzetti
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)
Download or read book Quadrature Formulae written by Aldo Ghizzetti and published by . This book was released on 1970 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert N. Desmarais
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (31 download)
Download or read book Programs for Computing Abscissas and Weights for Classical and Nonclassical Gaussian Quadrature Formulas written by Robert N. Desmarais and published by . This book was released on 1975 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel Solin
Publisher : CRC Press
ISBN 13 : 0203488040
Total Pages : 404 pages
Book Rating : 4.2/5 (34 download)
Download or read book Higher-Order Finite Element Methods written by Pavel Solin and published by CRC Press. This book was released on 2003-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Author : Alfio Quarteroni
Publisher : Springer Science & Business Media
ISBN 13 : 3642124305
Total Pages : 379 pages
Book Rating : 4.6/5 (421 download)
Download or read book Scientific Computing with MATLAB and Octave written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2010-05-30 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.
Author : Adhemar Bultheel
Publisher : Cambridge University Press
ISBN 13 : 0521650062
Total Pages : 423 pages
Book Rating : 4.5/5 (216 download)
Download or read book Orthogonal Rational Functions written by Adhemar Bultheel and published by Cambridge University Press. This book was released on 1999-02-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.
Author : R. Piessens
Publisher : Springer Science & Business Media
ISBN 13 : 3642617867
Total Pages : 311 pages
Book Rating : 4.6/5 (426 download)
Download or read book Quadpack written by R. Piessens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua tion of integrals. However, most routine integrals in practical scien tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.
Author : Milton Abramowitz
Publisher : Courier Corporation
ISBN 13 : 9780486612720
Total Pages : 1068 pages
Book Rating : 4.6/5 (127 download)
Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems
Author : Kenneth L. Judd
Publisher : MIT Press
ISBN 13 : 0262547740
Total Pages : 657 pages
Book Rating : 4.2/5 (625 download)
Download or read book Numerical Methods in Economics written by Kenneth L. Judd and published by MIT Press. This book was released on 2023-04-04 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.
Author : Helmut Brass
Publisher : American Mathematical Soc.
ISBN 13 : 0821853619
Total Pages : 376 pages
Book Rating : 4.8/5 (218 download)
Download or read book Quadrature Theory written by Helmut Brass and published by American Mathematical Soc.. This book was released on 2011-10-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.
Author : BRASS
Publisher : Birkhäuser
ISBN 13 : 3034863381
Total Pages : 382 pages
Book Rating : 4.0/5 (348 download)
Download or read book Numerical Integration IV written by BRASS and published by Birkhäuser. This book was released on 2013-11-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Madan Mohan Panja
Publisher : CRC Press
ISBN 13 : 0429534280
Total Pages : 466 pages
Book Rating : 4.4/5 (295 download)
Download or read book Wavelet Based Approximation Schemes for Singular Integral Equations written by Madan Mohan Panja and published by CRC Press. This book was released on 2020-06-07 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Author : V. I. Krylov
Publisher : Courier Corporation
ISBN 13 : 048615467X
Total Pages : 372 pages
Book Rating : 4.4/5 (861 download)
Download or read book Approximate Calculation of Integrals written by V. I. Krylov and published by Courier Corporation. This book was released on 2012-01-27 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.
