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Ebook: Nonlinear Numerical Methods and Rational Approximation II

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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.








Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Zeros of Orthogonal and Biorthogonal Polynomials: Some Old, Some New....Pages 3-15
Some Sequences Arising in the Creation of New Orthogonal Polynomials....Pages 17-24
Orthogonality and Boundary Interpolation....Pages 25-35
Breakdowns In The Computation Of Orthogonal Polynomials....Pages 37-47
Recurrence Relations in the Table of Vector Orthogonal Polynomials....Pages 49-59
Gegenbauer-Sobolev Orthogonal Polynomials....Pages 61-69
Inverse Problems: Rational Modifications....Pages 71-82
Normality and Error Formulae for Simultaneous Rational Approximants to Nikishin Systems....Pages 83-96
Front Matter....Pages 97-105
The Multipoint Pad? Table and General Recurrences for Rational Interpolation....Pages 107-107
Matrix Rational Interpolation with Poles as Interpolation Points....Pages 109-135
Pad?-Type Approximants and Multivariate Polynomial Interpolation....Pages 137-148
Front Matter....Pages 149-156
Behavior of Alternation Points in Best Rational Approximation....Pages 157-157
Asymptotics and Super Asymptotics for Best Rational Approximation Error Norms to the Exponential Function (The ‘1/9’ Problem) by the Carath?odory-Fej?r Method....Pages 159-172
An Approximation Method Based on the Second Kind Chebyshev Polynomials....Pages 173-185
Front Matter....Pages 187-199
On the Extension of Eiermann’s Theorem to Several Complex Variables....Pages 201-216
Linearization of Polynomial Maps and Singularity Analysis With Extended Precision Pad? Approximants....Pages 217-217
On Algebraic Computation of Number of Poles of Meromorphic Functions in the Unit Disk....Pages 219-228
Front Matter....Pages 229-236
A Comparison of Acceleration Techniques Applied to the Sor Method....Pages 237-240
Hermite-Pad? Polynomials and Approximation Properties....Pages 241-246
On the Efficiency of Linear But Nonregular Sequence Transformations....Pages 217-217
The Accuracy-Through-Order and the Equivalence Properties in the Algebraic Approximant *....Pages 247-260
On the Vector-Valued Pad? Approximants and the Vector ?-Algorithm....Pages 261-268
Quadrature Formulas on the Unit Circle and Two-Point Pad? Approximation....Pages 269-282
Front Matter....Pages 283-289
A Survey of Truncation Error Analysis for Pad? and Continued Fraction Approximants....Pages 291-301
Truncation Error Bounds For Limit K-Periodic Continued Fractions....Pages 303-317
Continued Fractions for the Symmetric Strong Stieltjes Moment Problem....Pages 319-319
Observations on Indeterminate Stieltjes Moment Problems....Pages 321-373
A Family of Classical Determinate Stieltjes Moment Problems with Discrete Solutions....Pages 375-385
Convergence Criteria of Two-Dimensional Continued Fractions....Pages 387-394
First-Order Linear Recurrence Systems and General N-Fractions....Pages 395-407
....Pages 409-422
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