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. Front Matter....Pages i-xlvi Gauss Elimination by Segments and Multivariate Polynomial Interpolation....Pages 1-22 Quantization of the Gamma Function....Pages 23-28 Vector Orthogonal Polynomials of Dimension - d ....Pages 29-39 An Extension of a Result of Rivlin on Walsh Equiconvergence (Faber Nodes)....Pages 41-66 The Parallel Solution of Ordinary Differential Equations and Some Special Functions....Pages 67-76 An Adaptive Semi-Iterative Method for Symmetric Semidefinite Linear Systems....Pages 77-96 A Unified Approach to Recurrence Algorithms....Pages 97-120 Quasi-Interpolation on Irregular Points....Pages 121-135 A Multigrid FFT Algorithm for Slowly Convergent Inverse Laplace Transforms....Pages 137-156 Sharp Bounds for the Lebesgue Constant in Quadratic Nodal Spline Interpolation....Pages 157-168 On the Error of Extended Gaussian Quadrature Formulae for Functions of Bounded Variation....Pages 169-178 Simultaneous Diagonalization Algorithms with Applications in Multivariate Statistics....Pages 179-205 On Some Approximations for the Zeros of Jacobi Polynomials....Pages 207-218 Prediction and the Inverse of Toeplitz Matrices....Pages 219-229 Stable Look-Ahead Versions of the Euclidean and Chebyshev Algorithms....Pages 231-260 On the Approximation of Univalent Functions by Subordinate Polynomials in the Unit Disk....Pages 261-271 Solutions to the Associated q -Askey-Wilson Polynomial Recurrence Relation....Pages 273-284 From Schrödinger Spectra to Orthogonal Polynomials Via a Functional Equation....Pages 285-307 Inequalities and Monotonicity Properties for Gamma and q -Gamma Functions....Pages 309-323 Bounds for Remainder Terms in Szegö Quadrature on the Unit Circle....Pages 325-342 Approximation of Integrals by Arithmetic Means and Related Matters....Pages 343-352 Using Quasi-Interpolants in a Result of Favard....Pages 353-357 Null Rules and Orthogonal Expansions....Pages 359-370 Some Differential Equations Satisfied by Hypergeometric Functions....Pages 371-381 On Mean Convergence of Lagrange-Kronrod Interpolation....Pages 383-396 Finite-Part Integrals and the Euler-Maclaurin Expansion....Pages 397-407 Approximation of Functions by Extended Lagrange Interpolation....Pages 409-420 Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas....Pages 421-434 Using the Matrix Refinement Equation for the Construction of Wavelets II: Smooth Wavelets on [0,1]....Pages 435-457 Summation of Series and Gaussian Quadratures....Pages 459-475 On a Singular Perturbation Problem....Pages 477-484 An Overview of Results on the Existence or Nonexistence and the Error Term of Gauss-Kronrod Quadrature Formulae....Pages 485-496 The Generalized Exponential Integral....Pages 497-510 On the Computation of the Zeros of the Bessel Polynomials....Pages 511-534 Some Properties of Polynomials Bounded at Equally Spaced Points....Pages 535-542 Numerical Methods via Transformations....Pages 543-550 Computational Aspects of Incomplete Gamma Functions with Large Complex Parameters....Pages 551-562 Sensitivity Analysis for Computing Orthogonal Polynomials of Sobolev Type....Pages 563-576 Back Matter....Pages 577-593 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 artiƯ 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 sesƯ 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 symƯ posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants