Pade and Rational Approximation
Theory and Applications
Published on 9. May 2013
506 pages
978-0-323-14777-4 (ISBN)
Description
Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications.
This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by "Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions.
This book is of great benefit to mathematicians, physicists, and laboratory workers.
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Content
List of Contributors and Participants Preface Theory of Padé Approximants and Generalizations Padé Approximants and Orthogonal Polynomials Convergence along Steplines in a Generalized Padé Table N-Variable Rational Approximants Asymptotic Behavior of the Zeros of Sequences of Padé Polynomials Confirming the Accuracy of Padé Table Approximants Laurent, Fourier, and Chebyshev-Padé Tables Generalisations of the Theorem of de Montessus Using Canterbury Approximants Rational Approximation by an Interpolation Procedure in Several Variables The Convergence of Padé Approximants to Functions with Branch Points Padé Approximants and Indefinite Inner Product Spaces The Transformation of Series by the Use of Padé Quotients and More General ApproximantsSpecial Functions and Continued Fractions A Relationship between Lie Theory and Continued Fraction Expansions for Special Functions Note on a Theorem of Saff and Varga Multiple-Point Padé Tables Application of Stieltjes Fractions to Birth-Death Processes On Geometric Characterizations of an Indeterminate Stieltjes Moment Sequence Rational Approximation to the Exponential Function On the Zeros and Poles of Padé Approximants to ez. II Two-Point Padé Tables, T-Fractions, and Sequences of Schur Three-Term Contiguous Relations and Some New Orthogonal PolynomialsTheory of Rational Approximations On a Problem of Saff and Varga Concerning Best Rational Approximation A Minimization Problem Related to Padé Synthesis of Recursive Digital Filters A Contribution to Rational Approximation on the Whole Real Line On the Possibility of Rational Approximation Geometric Convergence of Chebyshev Rational Approximations on the Half Line Optimal Approximation by "Almost Classical" Interpolation Approximation by Incomplete Polynomials (Problems and Results) On the Cardinality of a Set of Best Complex Rational Approximations to a Real Function Physical Applications The Application of Padé Approximants to Critical Phenomena Variational Principles and Matrix Padé Approximants Operator Padé Approximants for the Bethe-Salpeter Equation of Nucleon-Nucleon Scattering Series Summation Methods A Variational Approach to Operator and Matrix Padé Approximants. Applications to Potential Scattering and Field Theory Operator Padé Approximants and Three-Body Scattering Computations Software for Approximations or Approximation Theory as an Experimental Science Best Rational Approximation with Negative Poles to e-x on [0, 8] 413 Algorithms for Rational Approximations for the Gaussian Hypergeometric Function On the Limitation and Application of Padé Approximation to the Matrix Exponential Statistical Roundoff Error Analysis of a Padé Algorithm for Computing the Matrix Exponential Open Problems Summary of Panel Discussion Minimal Realization from Data Sets-A Problem of Rational Approximation Some Directions for Gun Fire Control Predictors Some Open Problems Concerning Polynomials and Rational Functions Rational Approximation at White Sands Missile Range
