Recent Advances in Numerical Analysis

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

Carl De Boor, Gene H. Golub

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780122083600
• eBook ISBN:
  9781483267111
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

• Front Cover
• Recent Advances in Numerical Analysis
• Copyright Page
• Table of Contents
• Contributors
• Preface
• Chapter 1. Positive Functions and Some Applications to Stability Questions for Numerical Methods
• Chapter 2. Constructive Polynomial Approximation in Sobolev Spaces
• Chapter 3. Questions of Numerical Condition Related to Polynomials
• Chapter 4. Global Homotopies and Newton Methods
• Chapter 5. Problems with Different Time Scales
• Chapter 6. Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations
• Chapter 7. Finite Element Approximations to the One-Dimensional Stefan Problem
• Chapter 8. The Hodie Method and Its Performance for Solving Elliptic Partial Differential Equations
• Chapter 9. Solving ODE's with Discrete Data in SPEAKEASY
• Chapter 10. Perturbation Theory for the Generalized Eigenvalue Problem
• Chapter 11. Some Remarks on Good, Simple, and Optimal Quadrature Formulas
• Chapter 12. Linear Differential Equations and Kronecker's Canonical Form
• Index