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

Topics in Numerical Analysis II

1st Edition

Editor: 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



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


No. of pages:
© Academic Press 1975
1st January 1975
Academic Press
eBook ISBN:

About the Editor

John J.H. Miller

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