Quadratic Alternating Direction Implicit Iteration for the
Fast Solution of Algebraic Riccati Equations
Quadratic Alternating Direction Implicit Iteration for the
Fast Solution of Algebraic Riccati Equations
N. Wong and V. Balakrishnan
In Proc. 2005 International Symposium on Intelligent Signal
Processing and Communication Systems (ISPACS),
Hong Kong, December 2005
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.
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