On the generation of algorithms for linear transforms and systems with symmetry

For many applications, especially from digital signal processing, linear maps must be applied frequently. This amounts to computing matrix-vector multiplications. To achieve real-time performance, it is essential to have fast algorithms. Many of the matrices that come up in the applications have a lot of structure that can be exploited to reduce the number of scalar operations to be performed in order to multiply with these matrices. This article is concerned with the case when this structure can be characterized by a special kind of symmetry. Its main objective is to describe how such a symmetry can be used to obtain a factorization of the matrix with all factors being sparse. Such a factorization yields an algorithm for multiplying with the matrix. In the literature various ways of applying one linear transform through another one by doing some minor extra calculations have been published. A well known example of this is the application of the Fourier transform via the Hartely transform. A further results presented here is a theoretical explanation for this on the basis of a relation on the symmetries of the involved transforms. The methods have been used to automatically generate fast algorithms for many of the transforms and filters from digital signal processing. The resulting algorithms compare well with manually derived ones from the literature. (orig.)SIGLEAvailable from TIB Hannover: RR 631(1997,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

VERMEIL. Verfahren und Methoden zur wissensbasierten Entwicklung zur wissensbasierten Entwicklung zuverlaessiger Leitanlagen Abschlussbericht

A simulator for technological processes has been specified and implemented in ELLA. Thereby, some of the well-known problems concerning the description of technological processes and hardware could be solved by a new approach. To this, we mention the description of general loops, the verification and the portation on arbitrary architectures (e.g. SMP, FPGA, ASIC). The grinding circuit of a cement mill has been modeled and, based on it, a simulation has been implemented. This has been made by using a physical modeling approach as well as means from system identification from real process data. Important, missing data has been determined approximately by suitable techniques. The simulation runs stable in the working scope and supplies adequate process values. (orig.)SIGLEAvailable from TIB Hannover: RB 631(1998,2)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Bildung, Wissenschaft, Forschung und Technologie, Bonn (Germany)DEGerman

Basic algorithms for rational function fields

By means of Groebner basis techniques algorithms for solving various problems concerning subfields K(g):=K(g_1,..., g_m) of a rational function field K(x):=K(x_1,..., x_n) are derived: computing canonical generating sets, deciding field membership, computing the degree and separability degree resp. the transcendence degree and a transcendence basis of K(x)/K(g), deciding whether f element of K(x) is algebraic or transcendental over K(g), computing minimal polynomials, and deciding whether K(g) contains elements of a 'particular structure', e.g., monic univariate polynomials of fixed degree. The essential idea is to reduce these problems to questions concerning an ideal of a polynomial ring; in the last section connections between minimal primary decompositions of this ideal and intermediate fields of K(g) and K(x) are given. (orig.)SIGLEAvailable from TIB Hannover: RR 631(1997,2) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Bibliography on expert systems and their methodology

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman