Approximation and Computation: A Festschrift in Honor of Walter Gautschi: Proceedings of the Purdue Conference, December 2–5, 1993(119 International Series of Numerical Mathematics)

R. V. M. Zahar* The sixty-fifth birthday of Walter Gautschi provided an opportune moment for an international symposium in his honor, to recognize his many contributions to mathematics and computer sciences. Conceived by John Rice and sponsored by Purdue University, the conference took place in West Lafayette from December 2 to 5, 1993, and was organized around the four main themes representing Professor Gautschi's principal research interests: Approximation, Orthogonal Polynomials, Quadrature and Special Functions. Thirty-eight speakers - colleagues, co-authors, research collaborators or doctoral students of Professor Gautschi - were invited to present articles at the conference, their lectures providing an approximately equal representation of the four disciplines. Five invited speakers, Germund Dahlquist, Philip Davis, Luigi Gatteschi, Werner Rheinboldt and Stephan Ruscheweyh, were unable to present their talks because of illness or other commitments, although Professors Dahlquist, Gatteschi and Ruscheweyh subsequently contributed arti­ cles to these proceedings. Thus, the final program contained thirty-three technical lectures, ten of which were plenary sessions. Approximately eighty scientists attended the conference, and for some ses­ sions - in particular, Walter's presentation of his entertaining and informative Reflections and Recollections - that number was complemented by many visitors and friends, as well as the family of the honoree. A surprise visit by Paul Erdos provided one of the highlights of the conference week. The ambiance at the sym­ posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants.

Table of Contents:
Gauss Elimination by Segments and Multivariate Polynomial Interpolation.- Quantization of the Gamma Function.- Vector Orthogonal Polynomials of Dimension — d.- An Extension of a Result of Rivlin on Walsh Equiconvergence (Faber Nodes).- The Parallel Solution of Ordinary Differential Equations and some Special Functions.- An Adaptive Semi-iterative Method for Symmetric Semidefinite Linear Systems.- A Unified Approach to Recurrence Algorithms.- Quasi-Interpolation on Irregular Points.- A Multigrid FFT Algorithm for Slowly Convergent Inverse Laplace Transforms.- Sharp Bounds for the Lebesgue Constant in Quadratic Nodal Spline Interpolation.- On the Error of Extended Gaussian Quadrature Formulae for Functions of Bounded Variation.- Simultaneous Diagonalization Algorithms.- On Some Approximations for the Zeros of Jacobi Polynomials.- Prediction and the Inverse of Toeplitz Matrices.- Stable Look-Ahead Versions of the Euclidean and Chebyshev Algorithms.- On the Approximation of Univalent Functions by Subordinate Polynomials in the Unit Disk.- Solutions to the Associated q-Askey-Wilson Polynomial Recurrence Relation.- From Schrödinger Spectra to Orthogonal Polynomials Via a Functional Equation.- Inequalities and Monotonicity Properties for Gamma and q-Gamma Functions.- Bounds for Remainder Terms in Szegö Quadrature on the Unit Circle.- Approximation of Integrals by Arithmetic Means and Related Matters.- Using Quasi-Interpolants in a Result of Favard.- Null Rules and Orthogonal Expansions.- Some Differential Equations Satisfied by Hypergeometric Functions.- On Mean Convergence of Lagrange-Kronrod Interpolation.- Finite-Part Integrals and the Euler-Maclaurin Expansion.- Approximation of Functions by Extended Lagrange Interpolation.- Error Estimates for Gauss-Laguerre andGauss-Hermite Quadrature Formulas.- Using the Matrix Refinement Equation for the Construction of Wavelets II: Smooth Wavelets on [0, 1].- Summation of Series and Gaussian Quadratures.- On a Singular Perturbation Problem.- An Overview of Results on the Existence or Nonexistence and the Error Term of Gauss-Kronrod Quadrature Formulae.- The Generalized Exponential Integral.- On the Computation of the Zeros of the Bessel Polynomials.- Some Properties of Polynomials Bounded at Equally Spaced Points.- Numerical Methods via Transformations.- Computational Aspects of Incomplete Gamma Functions with Large Complex Parameters.- Sensitivity Analysis for Computing Orthogonal Polynomials of Sobolev Type.- Author index.