Geodesic
On a~numerical solution of matrix polynomial equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 2, pp. 151-162

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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. 
@article{SJVM_2001_4_2_a3,
     author = {E. V. Dulov and N. A. Andrianova},
     title = {On a~numerical solution of matrix polynomial equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {151--162},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a3/}
}
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E. V. Dulov; N. A. Andrianova. On a~numerical solution of matrix polynomial equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 2, pp. 151-162. http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a3/