On a numerical solution of matrix polynomial equations

E. V. Dulov, N. A. Andrianova

Ulyanovsk State University, Faculty of Mathematics and Mechanics

Abstract: In this paper, we propose some direct and iterative algorithms for the solution of matrix polynomial equations of the form $AX+AX^2+\dots+AX^n=C$. A local convergence theorem of iterative algorithms is given, and the restrictions involved by this theorem are discussed. We give an estimation of convergence speed for these methods and make a number of useful notes for it's effective numerical implementation. Explicitly we discuss a special case, arising in problems of parameter estimation of linear dynamic stochastic systems.

UDC: 519.852

Received: 11.05.2000
Revised: 17.08.2000

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