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Quadratic operator equations and periodic operator continued fractions
Journal article   Open access   Peer reviewed

Quadratic operator equations and periodic operator continued fractions

Robert C. Busby and Wyman Fair
Journal of computational and applied mathematics, v 54(3), pp 377-387
1994
DOI: https://doi.org/10.1016/0377-0427(94)90258-5
url
https://doi.org/10.1016/0377-0427(94)90258-5View
Published, Version of Record (VoR)Open Access (Publisher-Specific),  Open

Abstract

Continued fraction Control theory Matrix Riccati equation
Conditions are given that assure convergence of an operator-valued periodic continued fraction of period two. These results and techniques are applied to get a solution of the quadratic operator equation in a complex Hilbert space. Special attention is then given to the important case of the quadratic matrix equation connected with the steady-state solution of the matrix Riccati equation from control theory. It is shown that a modification of the traditional matrix power approximation technique leads to a new, efficient and highly simplified method of approximating the unique nonnegative definite solution that exists in many important special cases.

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Mathematics, Applied
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