Solving quadratic matrix equations and factoring polynomials: new fixed point iterations based on Schur complements of Toeplitz matrices
Dario A. Bini, Luca Gemignani · Numerical Linear Algebra with Applications · 2004
Abstract A new class of functional iterations is introduced for the numerical solution of the matrix equation C+AX+BX2=0 where A,B,C are given m × m matrices and X is the unknown matrix. Each iteration in this class is globally convergent, self‐correcting, and the local convergence is linear with an arbitrarily large speed. The new iterations, which rely on the properties of Schur complements of block tridiagonal block Toeplitz matrices, overcome the problems encountered by quadratically convergent methods, like cyclic reduction, in the case of numerical singularity situations. Copyright © 2004 John Wiley & Sons, Ltd.