Ebook: Approximation and Computation: A Festschrift in Honor of Walter Gautschi: Proceedings of the Purdue Conference, December 2–5, 1993

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.

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Content:
Front Matter....Pages i-xlvi
Gauss Elimination by Segments and Multivariate Polynomial Interpolation....Pages 1-22
Quantization of the Gamma Function....Pages 23-28
An Extension of a Result of Rivlin on Walsh Equiconvergence (Faber Nodes)....Pages 29-39
The Parallel Solution of Ordinary Differential Equations and Some Special Functions....Pages 41-66
An Adaptive Semi-Iterative Method for Symmetric Semidefinite Linear Systems....Pages 67-76
A Unified Approach to Recurrence Algorithms....Pages 77-96
Quasi-Interpolation on Irregular Points....Pages 97-120
A Multigrid FFT Algorithm for Slowly Convergent Inverse Laplace Transforms....Pages 121-135
Sharp Bounds for the Lebesgue Constant in Quadratic Nodal Spline Interpolation....Pages 137-156
On the Error of Extended Gaussian Quadrature Formulae for Functions of Bounded Variation....Pages 157-168
Simultaneous Diagonalization Algorithms with Applications in Multivariate Statistics....Pages 169-178
On Some Approximations for the Zeros of Jacobi Polynomials....Pages 179-205
Prediction and the Inverse of Toeplitz Matrices....Pages 207-218
Stable Look-Ahead Versions of the Euclidean and Chebyshev Algorithms....Pages 219-229
On the Approximation of Univalent Functions by Subordinate Polynomials in the Unit Disk....Pages 231-260
Solutions to the Associated q-Askey-Wilson Polynomial Recurrence Relation....Pages 261-271
From Schr?dinger Spectra to Orthogonal Polynomials Via a Functional Equation....Pages 273-284
Inequalities and Monotonicity Properties for Gamma and q-Gamma Functions....Pages 285-307
Bounds for Remainder Terms in Szeg? Quadrature on the Unit Circle....Pages 309-323
Approximation of Integrals by Arithmetic Means and Related Matters....Pages 325-342
Using Quasi-Interpolants in a Result of Favard....Pages 343-352
Null Rules and Orthogonal Expansions....Pages 353-357
Some Differential Equations Satisfied by Hypergeometric Functions....Pages 359-370
On Mean Convergence of Lagrange-Kronrod Interpolation....Pages 371-381
Finite-Part Integrals and the Euler-Maclaurin Expansion....Pages 383-396
Approximation of Functions by Extended Lagrange Interpolation....Pages 397-407
Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas....Pages 409-420
Using the Matrix Refinement Equation for the Construction of Wavelets II: Smooth Wavelets on [0,1]....Pages 421-434
Summation of Series and Gaussian Quadratures....Pages 435-457
On a Singular Perturbation Problem....Pages 459-475
An Overview of Results on the Existence or Nonexistence and the Error Term of Gauss-Kronrod Quadrature Formulae....Pages 477-484
The Generalized Exponential Integral....Pages 485-496
On the Computation of the Zeros of the Bessel Polynomials....Pages 497-510
Some Properties of Polynomials Bounded at Equally Spaced Points....Pages 511-534
Numerical Methods via Transformations....Pages 535-542
Computational Aspects of Incomplete Gamma Functions with Large Complex Parameters....Pages 543-550
Sensitivity Analysis for Computing Orthogonal Polynomials of Sobolev Type....Pages 551-562
Back Matter....Pages 563-576
....Pages 577-593