Output details

Nearest common root of polynomials, approximate Greatest Common Divisor and the structured singular value, accepted

Robust control techniques and especially the structural singular values are used for the first time for the computation of the approximate greatest common divisor (GCD) of two polynomials. This is expressed as the distance from structured matrices of fixed rank and also generalises the notion of structured singular value of the matrix. The definition of approximate GCD allows the development, of many applications in numerical analysis, control and signal processing, such as stabilisation, blind de-convolution of constant modulus signals, decoding algorithms, etc., when the data are subjected to uncertainty due to noise, model uncertainty and finite-precision effects.