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Living Reference Work Entry In depth
Semi- and Quasi-separable Systems
The main objects of this chapter are “semi-separable systems,” sometimes called “quasi-separable systems.” These are systems of equations, in which the operator has a special structure, called “semi-separable”...
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Article
Interpolation and approximation of quasiseparable systems: the Schur-Takagi case
We explore how the classical Schur-Takagi interpolation theory as developed by Chamfy, Krein and Langer and Alpay, Azizov, Dijksma, and Langer generalizes to the matrix/operator case in the context of quasisep...
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Chapter and Conference Paper
Fast Stable Solver for Sequentially Semi-separable Linear Systems of Equations
In this paper we will present a fast backward stable algorithm for the solution of certain structured matrices which can be either sparse or dense. It essentially combines the fast solution techniques for band...
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Article
On the Hankel-norm approximation of upper-triangular operators and matrices
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Chapter
Reduction and Approximation of Linear Computational Circuits
In this tutorial, we present a survey of recent results on the approximation of matrices and operators with siblings of lower complexity. Our main method will be ‘approximation via interpolation’. The approach...
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Chapter
A New Space Partitioning for Map** Computations of the Radiosity Method onto a Highly Pipelined Parallel Architecture
Despite the fact that realistic images can be generated by ray-tracing and radiosity shading, these techniques are impractical for scenes of high complexity because of the extremely high time cost. Several att...
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Chapter and Conference Paper
Approximate Inversion of Partially Specified Positive Definite Matrices
A fast algorithm is presented that can be used to compute an approximate inverse of a positive definite matrix that is specified only on a multiple band. The approximate inverse is the inverse of a matrix that...
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Chapter and Conference Paper
A Hardware Algorithm for Fast Realistic Image Synthesis
A VLSI oriented algorithm, for the implementation of a generalized two-pass radiosity method is presented. The method allows any reflection behavior, varying from purely diffuse to perfect mirroring. Moreover,...
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Chapter
Inversion of Partially Specified Positive Definite Matrices by Inverse Scattering
Inverse scattering techniques such as the Wiener-Hopf factorization and the Schur algorithm can be used to determine an approximate inverse of a partially specified positive definite matrix. In this paper we e...
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Chapter
Inversion of Partially Specified Positive Definite Matrices by Inverse Scattering
Inverse scattering techniques such as the Wiener-Hopf factorization and the Schur algorithm can be used to determine an approximate inverse of a partially specified positive definite matrix. In this paper we e...
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Chapter
The Generalized Schur Algorithm: Approximation and Hierarchy
The generalized Schur algorithm as applied on a (full and large) strictly positive definite matrix yields an approximative inverse, which is block-band structured (has block-band support), and is such that its...
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Chapter and Conference Paper
Approximative Inversion of Positive Matrices with Applications to Modelling
An algorithm is presented to invert a (large and full) positive matrix approximatively, based on a (generalized) band of data centered around the diagonal. The approximative inverse is also positive with its o...
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Chapter and Conference Paper
Orthogonal filters: A numerical approach to filtering theory
In this paper we discuss orthogonal filter realization theory. An orthogonal filter is a device in which no other numerical operations occur but orthogonal transformations of coordinates. In its most elementar...
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Chapter and Conference Paper
Spectral approximation and estimation with scattering functions
In this paper an introduction is given to multiport scattering methods and their application to the estimation problem. Starting out from the theory of Darlington synthesis we derive fundamental solutions for ...
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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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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
Inverse Scattering and Linear Prediction, the Time Continuous Case
Let be given a scalar, stationary stochastic process y(t) with covariance function
(1.1) $$\delta (t) + k(\|t\|)$$ ... -
Chapter and Conference Paper
L2 Systems Theory: Some Applications
Some applications of L2 systems theory are presented in this paper. We will show how the technique of coprime factorization on which the L2 systems theory rests can be used directly to solve problems in other are...
