Recent Advances in Numerical Analysis - 1st Edition - ISBN: 9780122083600, 9781483267111

Recent Advances in Numerical Analysis

1st Edition

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, May 22-24, 1978

Editors: Carl De Boor Gene H. Golub
eBook ISBN: 9781483267111
Imprint: Academic Press
Published Date: 28th December 1978
Page Count: 282
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Description

Recent Advances in Numerical Analysis provides information pertinent to the developments in numerical analysis. This book covers a variety of topics, including positive functions, Sobolev spaces, computing paths, partial differential equations, and perturbation theory.

Organized into 12 chapters, this book begins with an overview of stability conditions for numerical methods that can be expressed in the form that some associated function is positive. This text then examines the polynomial approximation theory having applications to finite element Galerkin methods. Other chapters consider the numerical condition of polynomials by examining three particular problem areas, namely, the representation of polynomials, algebraic equations, and the problem of orthogonalization. This book discusses as well a general theory that leads to a systematic way to prepare the initial data. The final chapter deals with the derivation of the Kronecker canonical form.

This book is a valuable resource for applied mathematicians, numerical analysts, physicists, engineers, and research workers.

Table of Contents


Contributors

Preface

Positive Functions and Some Applications to Stability Questions for Numerical Methods

Constructive Polynomial Approximation in Sobolev Spaces

Questions of Numerical Condition Related to Polynomials

Global Homotopies and Newton Methods

Problems with Different Time Scales

Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations

Finite Element Approximations to the One-Dimensional Stefan Problem

The Hodie Method and Its Performance for Solving Elliptic Partial Differential Equations

Solving ODE's with Discrete Data in SPEAKEASY

Perturbation Theory for the Generalized Eigenvalue Problem

Some Remarks on Good, Simple, and Optimal Quadrature Formulas

Linear Differential Equations and Kronecker's Canonical Form

Index

Details

No. of pages:
282
Language:
English
Copyright:
© Academic Press 1978
Published:
Imprint:
Academic Press
eBook ISBN:
9781483267111

About the Editor

Carl De Boor

Gene H. Golub