Computation of the least common multiple of a set of polynomials: symbolic and numerical approaches

The problem of computing the least common multiple (LCM) of a set of polynomials is an integral part of algebraic synthesis methods in control theory. We investigate a number of alternative algebraic methodologies for computation of LCM, which can be performed symbolically, but can also lead to numerical algorithms for evaluation of exact, as well as approximate LCMs. The latter problem (approximate LCMs) is important especially when the problem data are not exact and thus the use of symbolic means does not seem to be appropriate. A new algebraic procedure with its symbolic and numerical implementations are presented, which make extensive use of new robust algorithms for computation of the greatest common divisor (GCD) of a set of polynomials