Bekhiti, BelkacemDahimene, AbdelhakimHariche, KamelFragulis, George F.2020-12-172020-12-17201803248569https://arxiv.org/abs/1803.10557https://dspace.univ-boumerdes.dz/handle/123456789/5940In this paper we factorize matrix polynomials into a complete set of spectral factors using a new design algorithm and we provide a complete set of block roots (solvents). The procedure is an extension of the (scalar) Horner method for the computation of the block roots of matrix polynomials. The Block-Horner method brings an iterative nature, faster convergence, nested programmable scheme, needless of any prior knowledge of the matrix polynomial. In order to avoid the initial guess method we proposed a combination of two computational procedures. First we start giving the right Block-QD (Quotient Difference) algorithm for spectral decomposition and matrix polynomial factorization. Then the construction of new block Horner algorithm for extracting the complete set of spectral factors is given.Block rootsSolventsSpectral factorsBlock-Q.DalgorithmBlock-Horner’s algorithmMatrix polynomialArticle