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.
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
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- © Academic Press 1978
- 28th December 1978
- Academic Press
- eBook ISBN: