QUADRATIC OPERATOR-EQUATIONS AND PERIODIC OPERATOR CONTINUED FRACTIONS

[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.

[发布日期] 1994-10-20

[关键词] CONTINUED FRACTION;MATRIX RICCATI EQUATION;CONTROL THEORY