Ebook: Applications and Computation of Orthogonal Polynomials: Conference at the Mathematical Research Institute Oberwolfach, Germany March 22–28, 1998

The workshop on Applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th­ century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.

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Content:
Front Matter....Pages i-xiii
The Sensitivity of Least Squares Polynomial Approximation....Pages 1-19
Transpose-Free Look-Ahead Algorithms for Lanczos’ Method....Pages 21-40
Applications of Anti-Gauss Quadrature Rules in Linear Algebra....Pages 41-56
Stieltjes Polynomials and the Error of Gauss-Kronrod Quadrature Formulas....Pages 57-77
Fast Solution of Confluent Vandermonde-Like Linear Systems Using Polynomial Arithmetic....Pages 79-92
On Discrete Polynomial Least-Squares Approximation in Moving Time Windows....Pages 93-107
Quadrature Rules Based on s-Orthogonal Polynomials for Evaluating Integrals with Strong Singularities....Pages 109-119
Gegenbauer Weight Functions Admitting L 2 Duffin and Schaeffer Type Inequalities....Pages 121-131
Questions Related to Gaussian Quadrature Formulas and Two-Term Recursions....Pages 133-144
Construction and Computation of a New Set of Orthogonal Polynomials....Pages 145-151
Fourier Transforms of Orthogonal Polynomials of Singular Continuous Spectral Measures....Pages 153-163
On a Sequence of Fast Decreasing Polynomial Operators....Pages 165-178
M?ntz Orthogonal Polynomials and Their Numerical Evaluation....Pages 179-194
Positivity of Gauss-Kronrod Formulae for a Certain Ultraspherical Weight Function....Pages 195-202
A Christoffel-Darboux-Type Formula for Szeg? Polynomials and Polynomial Evaluation....Pages 203-216
Applications of Tensor-Valued Tri-Variate Hermite Polynomials and Spherical Harmonics in the Kinetic Theory of Gases....Pages 217-225
Indeterminate Moment Problems and a Conjecture on the Growth of the Entire Functions in the Nevanlinna Parametrization....Pages 227-237
Spectral Methods Based on Nonclassical Orthogonal Polynomials....Pages 239-251
Back Matter....Pages 253-273

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Content:
Front Matter....Pages i-xiii
The Sensitivity of Least Squares Polynomial Approximation....Pages 1-19
Transpose-Free Look-Ahead Algorithms for Lanczos’ Method....Pages 21-40
Applications of Anti-Gauss Quadrature Rules in Linear Algebra....Pages 41-56
Stieltjes Polynomials and the Error of Gauss-Kronrod Quadrature Formulas....Pages 57-77
Fast Solution of Confluent Vandermonde-Like Linear Systems Using Polynomial Arithmetic....Pages 79-92
On Discrete Polynomial Least-Squares Approximation in Moving Time Windows....Pages 93-107
Quadrature Rules Based on s-Orthogonal Polynomials for Evaluating Integrals with Strong Singularities....Pages 109-119
Gegenbauer Weight Functions Admitting L 2 Duffin and Schaeffer Type Inequalities....Pages 121-131
Questions Related to Gaussian Quadrature Formulas and Two-Term Recursions....Pages 133-144
Construction and Computation of a New Set of Orthogonal Polynomials....Pages 145-151
Fourier Transforms of Orthogonal Polynomials of Singular Continuous Spectral Measures....Pages 153-163
On a Sequence of Fast Decreasing Polynomial Operators....Pages 165-178
M?ntz Orthogonal Polynomials and Their Numerical Evaluation....Pages 179-194
Positivity of Gauss-Kronrod Formulae for a Certain Ultraspherical Weight Function....Pages 195-202
A Christoffel-Darboux-Type Formula for Szeg? Polynomials and Polynomial Evaluation....Pages 203-216
Applications of Tensor-Valued Tri-Variate Hermite Polynomials and Spherical Harmonics in the Kinetic Theory of Gases....Pages 217-225
Indeterminate Moment Problems and a Conjecture on the Growth of the Entire Functions in the Nevanlinna Parametrization....Pages 227-237
Spectral Methods Based on Nonclassical Orthogonal Polynomials....Pages 239-251
Back Matter....Pages 253-273
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