Approximate least common multiple of several polynomials using the ERES division algorithm

In this paper a numerical method for the computation of the approximate least common multiple (ALCM) of a set of several univariate real polynomials is presented. The most important characteristic of the proposed method is that it avoids root finding procedures and computations involving the greatest common divisor (GCD). Conversely, it is based on the algebraic construction of a special matrix which contains key data from the original set of polynomials and leads to the formulation of a linear system which provides the degree and the coefficients of the ALCM using low-rank approximation techniques and numerical optimization tools particularly in the presence of inaccurate data. The numerical stability and complexity of the method are analysed, and a comparison with other methods is provided.