Recent advances in numerical analysis : proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin--Madison, May 22-24, 1978

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. Content: Front Matter, Page iii Copyright, Page iv Contributors, Page vii Preface, Page ix, Carl de Boor, Gene H. Golub Dedication, Pages x-xi Positive Functions and some Applications to Stability Questions for Numerical Methods, Pages 1-29, Germund Dahlquist Constructive Polynomial Approximation in Sobolev Spaces, Pages 31-44, Todd Dupont, Ridgway Scott Questions of Numerical Condition Related to Polynomials, Pages 45-72, Walter Gautschi Global Homotopies and Newton Methods, Pages 73-94, Herbert B. Keller Problems with Different Time Scales, Pages 95-106, Heinz-Otto Kreiss Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations, Pages 107-117, Peter D. Lax Finite Element Approximations to the One Dimensional Stefan Problem, Pages 119-142, J.A. Nitsche The Hodie Method and its Performance for Solving Elliptic Partial Differential Equations, Pages 143-175, Robert E. Lynch, John R. Rice Solving ODE'S with Discrete Data in SPEAKEASY, Pages 177-192, L.F. Shampine Perturbation Theory for the Generalized Eigenvalue Problem, Pages 193-206, G.W. Stewart Some Remarks on Good, Simple, and Optimal Quadrature Formulas, Pages 207-229, H.F. Weinberger Linear Differential Equations and Kronecker's Canonical Form, Pages 231-265, J.H. Wilkinson Index, Pages 267-270 Conducted By The Mathematics Research Center, The University Of Wisconsin--madison, May 22-24, 1978 ; Edited By Carl De Boor And Gene H. Golub. Includes Bibliographies And Index.