Encyclopaedia of Mathematics
Volume 1 / 1995 to Volume 10 / 1994
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Article
A generalized eigenvalue problem for quasi-orthogonal rational functions
In general, the zeros of an orthogonal rational function (ORF) on a subset of the real line, with poles among $${\{\alpha_1,\ldots,\al...
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Book Series
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Book
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Article
The implicit application of a rational filter in the RKS method
The implicitly restarted Arnoldi method implicitly applies a polynomial filter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit filtering by rational functions is propose...
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Article
Orthogonal rational functions and modified approximants
Let {α n | n ∞ be a sequence in the open unit disk in the complex plane and let ...
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Article
On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle
We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [−π, π]. As a consequence, quadrature formulas arise...
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Chapter
Matrix Rational Interpolation with Poles as Interpolation Points
In this paper, we show the equivalence between matrix rational interpolation problems with poles as interpolation points and no-pole problems. This equivalence provides an effective method for computing matrix...
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Article
A general module theoretic framework for vector M-Padé and matrix rational interpolation
A general module theoretic framework is used to solve several classical interpolation problems and generalizations thereof in a unified way. These problems are divided into two main families. The first family ...
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Chapter and Conference Paper
On the block structure of the Laurent-Padé table
Some ideas on the block structure of a formal Laurent-Padé table will be given. The structure is derived from the block structure of the table of Toeplitz determinants which also defines the blocks of a classi...
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Chapter and Conference Paper
Applications of Pade approximants and continued fractions in systems theory
A brief introduction to the terminology of Padé approximation is given first. In the next sections we summarize some known applications of Padé approximants and continued fractions in the theory of linear syst...
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Chapter
Editorial
This special issue on rational approximations for systems presents a collection of papers which grew out of presentations held at a workshop at the Catholic University of Leuven in August 1981. The organizers ...
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Chapter and Conference Paper
Short Communications
One of the generalizations of the ordinary Padé table to simultaneous approximation of (formal) power series can be defined by:
given formal power series f1,..., fn and non-neg...
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Article
Special issue on rational approximations for systems
To conclude our discussion we can only confess to our shortcomings as organizers and editors. We have been incomplete, we have been biased, and, worst of all, we have not been able to produce the most essentia...
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Chapter and Conference Paper
Error analysis of incoming and outgoing schemes for the trigonometric moment problem
The solution of the trigonometric moment problem involves the computation of a (0/n) Laurent-Padé approximant for a positive real function on the complex unit circle. The incoming scheme is equivalent with the...
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Chapter and Conference Paper
Recursive algorithms for the Padé table : Two approaches
In [14], a relation is given between the Viskovatoff algorithm for the determination of continued fractions and the triangular factorization of Hankel matrices. In this paper this idea will be further devellop...
