Book Review: Polynomial and matrix computations
نویسندگان
چکیده
منابع مشابه
Fast Matrix Polynomial Computations
Pour une matrice polynomiale P(x) de degr e d dans Mn;n(Kx]), o u K est un corps commutatif, une r eduction a la forme normale d'Hermite peut ^ etre calcul ee en O ~ (M(nd)) op erations arithm etiques, si M(n) est le co^ ut du produit de deux matrices n n sur K. De plus, une telle r eduction peut ^ etre obtenue en temps parall ele O(log +1 (nd)) en utilisant O(L(nd)) processeurs, si le probl em...
متن کاملSolving Polynomial Systems by Matrix Computations
Two main approaches are used, nowadays, to compute the roots of a zero-dimensional polynomial system. The rst one involves Grrbner basis computation, and applies to any zero-dimensional system. But, it is performed with exact arithmetic and, usually, big numbers appear during the computation. The other approach is based on resultant formulations and can be performed with oating point arithmetic...
متن کاملBlock Toeplitz Methods in Polynomial Matrix Computations
Some block Toeplitz methods applied to polynomial matrices are reviewed. We focus on the computation of the structure (rank, null-space, infinite and finite structures) of an arbitrary rectangular polynomial matrix. We also introduce some applications of this structural information in control theory. All the methods outlined here are based on the computation of the null-spaces of suitable block...
متن کاملFast Error-free Algorithms for Polynomial Matrix Computations
Matrices of pol nomials over rings and fields provide a unifying framework $r many control system design problems. These include dynamic compensator design, infinite dimensional systems, controllers for nonlinear systems, and even controllers for discrete event s stems. An important obstacle for utilizing these owerful matiematical tools in practical applications has been &e non-availability of...
متن کاملNumerical Stability of Block Toeplitz Algorithms in Polynomial Matrix Computations
We study the problem of computing the eigenstructure of a polynomial matrix. Via a backward error analysis we analyze the stability of some block Toeplitz algorithms to obtain this eigenstructure. We also elaborate on the nature of the problem, i.e. conditioning and posedness. Copyright c ©2005 IFAC.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1995
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1995-00597-5