QUADRATIC OPERATOR-EQUATIONS AND PERIODIC OPERATOR CONTINUED FRACTIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:54

Article

BUSBY, RC ; FAIR, W

关键词: CONTINUED FRACTION;    MATRIX RICCATI EQUATION;    CONTROL THEORY;   

DOI  :  10.1016/0377-0427(94)90258-5

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free