Nonlinear Numerical Methods and Rational Approximation II

1. Front Matter

   Pages i-xviii

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2. Orthogonal Polynomials

   1. Front Matter

      Pages 1-1

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   2. Zeros of Orthogonal and Biorthogonal Polynomials: Some Old, Some New

      • D. S. Lubinsky

      Pages 3-15

   3. Some Sequences Arising in the Creation of New Orthogonal Polynomials

      • Jet Wimp, Harry Kiesel

      Pages 17-24

   4. Convergence of Lagrange Interpolation for Freud Weights in Weighted L _p (ℝ), 0 <P ≤ 1

      • D. M. Matjila

      Pages 25-35

   5. Orthogonality and Boundary Interpolation

      • Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njåstad

      Pages 37-47

   6. Breakdowns In The Computation Of Orthogonal Polynomials

      • C. Brezinski, M. Redivo-Zaglia

      Pages 49-59

   7. Recurrence Relations in the Table of Vector Orthogonal Polynomials

      • J. Van Iseghem

      Pages 61-69

   8. Gegenbauer-Sobolev Orthogonal Polynomials

      • Francisco Marcellán, Teresa E. Pérez, Miguel A. Piñar

      Pages 71-82

   9. Inverse Problems: Rational Modifications

      • A. Cachafeiro, C. Suárez

      Pages 83-96

   10. Normality and Error Formulae for Simultaneous Rational Approximants to Nikishin Systems

       • K. Driver, H. Stahl

       Pages 97-105

3. Rational Interpolation

   1. Front Matter

      Pages 107-107

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   2. The Multipoint Padé Table and General Recurrences for Rational Interpolation

      • Martin H. Gutknecht

      Pages 109-135

   3. Matrix Rational Interpolation with Poles as Interpolation Points

      • M. Van Barel, B. Beckermann, A. Bultheel, G. Labahn

      Pages 137-148

   4. Padé-Type Approximants and Multivariate Polynomial Interpolation

      • Paul Sablonnière

      Pages 149-156

4. Rational Approximation

   1. Front Matter

      Pages 157-157

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   2. Behavior of Alternation Points in Best Rational Approximation

      • D. Braess, D. S. Lubinsky, E. B. Saff

      Pages 159-172

   3. Asymptotics and Super Asymptotics for Best Rational Approximation Error Norms to the Exponential Function (The ‘1/9’ Problem) by the Carathéodory-Fejér Method

      • Alphonse P. Magnus

      Pages 173-185

   4. Frequency Weighted H ₂ Model Reduction

      • G. Schelfhout, P. Van Overschee, B. De Moor

      Pages 187-199

   5. An Approximation Method Based on the Second Kind Chebyshev Polynomials

      • M. Bozzini, M. Rossini

      Pages 201-216

These are the proceedings of the international conference on "Nonlinear numerical methods and Rational approximation II" organised by Annie Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70's. The following figures illustrate the growing number of participants and their geographical dissemination. In 1993 the Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerp), J. Meinguet (Louvain-Ia-Neuve) and J.-P. Thiran (Namur). The conference focused on the use of rational functions in different fields of Numer­ ical Analysis. The invited speakers discussed "Orthogonal polynomials" (D. S. Lu­ binsky), "Rational interpolation" (M. Gutknecht), "Rational approximation" (E. B. Saff) , "Pade approximation" (A. Gonchar) and "Continued fractions" (W. B. Jones). In contributed talks multivariate and multidimensional problems, applications and implementations of each main topic were considered. To each of the five main topics a separate conference day was devoted and a separate proceedings chapter compiled accordingly. In this way the proceedings reflect the organisation of the talks at the conference. Nonlinear numerical methods and rational approximation may be a nar­ row field for the outside world, but it provides a vast playground for the chosen ones. It can fascinate specialists from Moscow to South-Africa, from Boulder in Colorado and from sunny Florida to Zurich in Switzerland.

• Meromorphic function
• continued fraction
• differential equation
• exponential function
• numerical analysis
• numerical methods
• orthogonal polynomials

• Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

  Annie Cuyt

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