  In 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-Q. D. (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.
