Constructive Algebra and Systems Theory

Bernard Hanzon and Michiel Hazewinkel (eds.)

2006 | vi + 358 pagina's | ISBN 90-6984-477-X | Euro 65,00

This volume brings together contributions from well-known researchers in the field of constructive algebra and computer algebra on the one hand and systems theory, including multidimensional systems theory on the other hand. There has been a slow but steady increase in the usage of constructive algebra in systems theory. In multidimensional systems theory Gröbner basis techniques form an essential tool. During the last decade an important development in constructive algebra was the eigenvalue approach to the problem of solving a polynomial system of equations, pioneered by Stetter and others. It turns out that these techniques have a very natural interpretation in a state-space realization approach to multidimensional systems theory.

This volume contributes to the interaction between these fields. The authors make clear that there are many connections between constructive algebra and systems theory. The papers deal with theorem proving and quantifier elimination, applications to control theory, solving polynomial equations and algebraic optimization problems by matrix methods, applications to statistics, Gröbner basis methods and other constructive algebra methods, the interplay between computer algebra and multi-dimensional(or n-D) systems, applications of computer algebra to various kinds of modelling, and applications of differential algebra and differential geometry to systems theory.

The 22 articles in this volume demonstrate the exchange of information and interaction between the various theoretical and applied fields involved, which is vital for the developments on both sides.

Contributors: H. Anai, I. Brás, B. Buchberger, V.I. Elkin, M. Fliess, V.P. Gerdt, S.T. Glad, B. Hanzon, Sh. Hara, D. Jibetean, P.H.M. Kersten, A.H.M. Levelt, J.M. Maciejowski, B. Mourrain, U. Oberst, R. Peeters, H.K. Pillai, G. Pistone, P. Rapisarda, E. Riccomagno, L. Robbiano, P. Rocha, E. Rogers, H.J. Stetter, P. Vettori, J.C. Willems, F. Winkler, H.P. Wynn, J. Wood, S. Zampieri

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