Topics in Numerical Analysis II - 1st Edition - ISBN: 9780124969520, 9780323141345

Topics in Numerical Analysis II

1st Edition

Editors: John J.H. Miller
eBook ISBN: 9780323141345
Imprint: Academic Press
Published Date: 1st January 1975
Page Count: 280
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Topics in Numerical Analysis II contains in complete form, the papers given by the invited speakers to the Conference on Numerical Analysis held under the auspices of the National Committee for Mathematics of the Royal Irish Academy at University College, Dublin from 29th July to 2nd August, 1974. In addition, the titles of the contributed papers are listed together with the names and addresses of the authors who presented them at the conference. This book is divided into 20 chapters that present the papers in their entirety. They discuss such topics as applications of approximation theory to numerical analysis; interior regularity and local convergence of Galerkin finite element approximations for elliptic equations; and numerical estimates for the error of Gauss-Jacobi quadrature formulae. Some remarks on the unified treatment of elementary functions by microprogramming; application of finite difference methods to exploration seismology; and variable coefficient multistep methods for ordinary differential equations applied to parabolic partial differential equations are also presented. Other chapters cover realistic estimates for generic constants in multivariate pointwise approximation; matching of essential boundary conditions in the finite element method; and collocation, difference equations, and stitched function representations. This book will be of interest to practitioners in the fields of mathematics and computer science.

Table of Contents

Sponsors Preface Names and Addresses of Invited Speakers Titles and Authors of Contributed Papers Names and Addresses of Presenters of Contributed Papers On a Discretization of yn + ?yk = 0 Some Applications of Approximation Theory to Numerical Analysis Interior Regularity and Local Convergence of Galerkin Finite Element Approximations for Elliptic Equations Numerical Estimates for the Error of Gauss-Jacobi Quadrature Formula Some Remarks on the Unified Treatment of Elementary Functions by Microprogramming Application of Finite Difference Methods to Exploration Seismology Variable Coefficient Multistep Methods for Ordinary Differential Equations Applied to Parabolic Partial Differential Equations Realistic Estimates for Generic Constants in Multivariate Pointwise Approximation Matching of Essential Boundary Conditions in the Finite Element Method Collocation, Difference Equations, and Stitched Function Representations A New Approach to Matrix Theory or Many Facets of the Matrix Decomposition Theorem Hybrid Finite Element Methods for Solving 2nd Order Elliptic Equations Approximation of Fixed Points of Generalized Contraction Mappings The Use of Differential Inequalities in the Convergence Analysis of the Numerical Solution of Degenerate Parabolic Equations Hausdorff Approximation of Functions and Point Sets Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices Biconvergence, Instability and Consistency of One-Step Methods for the Numerical Solution of Initial Value Problems in Ordinary Differential Equations On the Error Estimation of Chebyshev Series Approximate Solutions to Boundary Value Problems Numerical Solution of Evolution Problems in Banach Spaces Unconditionally Stable Finite Element Schemes for Parabolic Equations Author Index


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© Academic Press 1975
Academic Press
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About the Editor

John J.H. Miller

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