This list of more than 2500 references has been gathered over the past 20 years, from the point of view that we want to study and reliably compute generalizations of Padé approximants. We also refer the reader to the following list of abbreviations in order to get an idea of the topics that are covered. The bibliography is in no way complete but rather a personal selection and reflects of course the availability of journals in our university library and libraries visited while traveling, as well as the succession of research themes and the correspondence with colleagues throughout the years.
Keywords:
Extrapolation techniques and Convergence acceleration , Some real-world industrial applications (use of rational approximants,, use of non-standard arithmetic), Computer arithmetic (none of the more specific keywords), Best (non-rational) approximation (uniform, least-squares, ...), Continued fraction material, Convergence problems: sequences of approximants, iterative, procedures, recursive schemes, Differential and Difference equations, also Differentiation, IEEE standard related material, Error analysis and Stability of numerical algorithms, Exact rational arithmetic, Floating-point computing and Floating-point arithmetic, standard, precisions and multiprecision, Implementation of Standard and Special functions, Fuzzy arithmetic, Fixpoint problems, Hardware related information, Integration and Integral equations, Interval arithmetic, Linear algebra material, Matrix (rational) approximation, Multivariate Pad approximation, Moment problems, Multivariate rational interpolation, Number theoretic results in the area, Solving a Nonlinear equation in one variable, Solving Nonlinear systems of equations, Object-oriented methodology (for numerics), Operator equations and Abstract spaces, Orthogonal polynomials (connection with Pad approximation), Polynomial techniques, as opposed to rational interpolation and, approximation, Performance considerations, Programming language material related to one of the other topics, Best rational approximation, Recursive computational techniques, Recurrence relations for Pad , approximants, continued fraction convergents, orthogonal polynomials,, Reliable computing, Validation, Symbolic-numeric algorithms, Accurate, expression evaluation, Floating-point testing, Scientific computation (general), Software, Routines, Programs, Algorithms etc., Splines, Surveys, Background material and Basic mathematics, Stochastic arithmetic, Summation of series and Series related material, Symbolic computing, Systems theory, Univariate Pade approximation, Univariate rational interpolation, Vector (rational) approximation, Expert Systems, Problem Solving Environments
Author Comments:
Thanks are due to: Gerd Neugebauer, author of BibTool, and Eyal Doron, author of BibDB, for their prompt reply to all our questions and the speedy implementation of some of our suggestions, to my daughter Annelies van Soom for helping me with the constant updating of the database of references, and last but certainly not least, to Stefan Becuwe for the conversion of the entire old database from Clipper to BibTeX with all its functionality, and for his invaluable support.
