Quadratic alternating direction implicit iteration for the fast solution of algebraic Riccati equations

Abstract

Algebraic Riccati equations (AREs) spread over many branches of signal processing and system design problems. Solution of large scale AREs, however, can be computationally prohibitive. This paper introduces a novel second order extension to the alternating direction implicit (ADI) iteration, called quadratic ADI or QADI, for the efficient solution of an ARE. QADI is simple to code and exhibits fast convergence. A Cholesky factor variant of QADI, called CFQADI, further accelerates computation by exploiting low rank matrices commonly found in physical system modeling. Application examples show remarkable efficiency and scalability of the QADI algorithms over conventional ARE solvers.