Topics in numerical analysis II [recurso electrónico] proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1974

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. Content: Sponsors , Page ii Front Matter , Page iii Copyright , Page iv Preface , Pages v-vi , John J.H. Miller Names and Addresses of Invited Speakers , Pages vii-viii Titles and Authors of Contributed Papers , Pages ix-x Names and Addresses of Presenters of Contributed Papers , Pages xi-xii On a Discretization of y ′′ + λ y k = 0 , Pages 1-15 , E.L. Allgower Some Applications of Approximation Theory to Numerical Analysis , Pages 17-25 , R. Ansorge Interior Regularity and Local Convergence of Galerkin Finite Element Approximations for Elliptic Equations , Pages 27-41 , J. Descloux Numerical Estimates for the Error of Gauss—Jacobi Quadrature Formulae , Pages 43-50 , Géza Freud Some Remarks on the Unified Treatment of Elementary Functions by Microprogramming , Pages 51-56 , Sin Hitotumatu Application of Finite Difference Methods to Exploration Seismology , Pages 57-76 , K.R. Kelly, R.M. Alford, S. Treitel, R.W. Ward Variable Coefficient Multistep Methods for Ordinary Differential Equations applied to Parabolic Partial Differential Equations , Pages 77-87 , J.D. Lambert Realistic Estimates for Generic Constants in Multivariate Pointwise Approximation , Pages 89-107 , Jean Meinguet Matching of Essential Boundary Conditions in the Finite Element Method , Pages 109-120 , A.R. Mitchell, J.A. Marshall Collocation, Difference Equations, and Stitched Function Representations , Pages 121-132 , M.R. Osborne A New Approach to Matrix Theory or Many Facets of the Matrix Decomposition Theorem , Pages 133-139 , Alladi Ramakrishnan, R. Jagannathan Hybrid Finite Element Methods for Solving 2nd Order Elliptic Equations , Pages 141-155 , P.A. Raviart Approximation of Fixed Points of Generalized Contraction Mappings , Pages 157-161 , Ioan A. Rus The Use of Differential Inequalities in the Convergence Analysis of the Numerical Solution of Degenerate Parabolic Equations , Pages 163-173 , E. Schechter Hausdorff Approximation of Functions and Point Sets , Pages 175-184 , Bl. Sendov Methods of Simultaneous Iteration for Calculating Eigenvectors of Matrices , Pages 185-196 , G.W. Stewart Biconvergence, Bistability and Consistency of One-Step Methods for the Numerical Solution of Initial Value Problems in Ordinary Differential Equations , Pages 197-211 , Friedrich Stummel On the Error Estimation of Chebyshev Series Approximate Solutions to Boundary Value Problems , Pages 213-242 , M. Urabe Numerical Solution of Evolution Problems in Banach Spaces , Pages 243-251 , Emil Vitásek, Jiří Taufer Unconditionally Stable Finite Element Schemes for Parabolic Equations , Pages 253-261 , Miloš Zlámal Author Index , Pages 263-266