ON COMPUTING HIGH ACCURACY SOLUTIONS OF A CLASS OF RICCATI EQUATIONS

摘要

The paper is concerned with the computation with high accuracy of the non-negative definite stabilizing solution of the matrix Riccati equation A~TX + XA + XQX + R = 0, where A is stable, Q = Q~T ≥ 0 and R = R~T ≥ 0. The limiting accuracy solution can be computed by using an iterative refinement technique based on Newton's method. A proof of global convergence of the iterative process, with final quadratic rate, is given. Several ways to compute with high accuracy the Cholesky factor of the solution are also discussed.