Approximate algebraic computations of algebraic invariants
N. Karcanias, Marilena Mitrouli · Institution of Engineering and Technology eBooks · 1999
This chapter deals with the computation of certain types and values of invariants, the presence of which on a family of linear models is nongeneric. The computation of such invariants on models with numerical inaccuracies requires special methods, which may lead to approximate meaningful results to the computation problem. A classification of the algebraic computations according to their behaviour on numerically uncertain models is given, and then two of the key problems underlying the computation of a number of system invariants are considered; these are the problems of approximate computations of the greatest common divisor (GCD) and least common multiple (LCM) of polynomials. Some fundamental issues in the transformation of the GCD and LCM algebraic computations in an analytic, 'approximate' sense are considered, and methodologies yielding approximate solutions to GCD, LCM problems are examined.