Polynomial roots: The ultimate answer? (Q1899387)

The authors present a procedure which is able to find all the roots of a polynomial along with the respective multiplicities. The procedure consists in the construction of a block diagonal matrix whose blocks are tridiagonal with only simple eigenvalues. The tridiagonal matrix may be constructed either numerically or formally. Once the block diagonal matrix is obtained, the order of convergence of the proposed procedure is that of the QR factorization method for tridiagonal matrices and for simple eigenvalues. Finally, some numerical results are analysed.