An algorithm for polynomial matrix factor extraction

An algorithm is described for extracting a polynomial matrix factor featuring any subset of the zeros of a given non-singular polynomial matrix. It is assumed that the zeros to be extracted are given as input data. Complex or repeated zeros are allowed. The algorithm is based on interpolation and relies upon numerically reliable subroutines only. It makes use of a procedure that computes the generalized characteristic vectors of a polynomial matrix at a given point. The extracted factor is provided in column- and row-reduced Popov form. Applications of the algorithm include polynomial matrix interpolation, plus/minus factorization, column- and row-reduction, or computation of the Smith form of a polynomial matrix. The numerical routines described in the paper are implemented in release 2.0 of the Polynomial Toolbox for MATLAB.