Abstract
Consider the computation of the solution for a class of discrete-time algebraic Riccati equations (DAREs) with the low-ranked coefficient matrix G and the high-ranked constant matrix H. A structured doubling algorithm is proposed for large-scale problems when A is of lowrank. Compared to the existing doubling algorithm of O(2kn) flops at the k-th iteration, the newly developed version merely needs O(n) flops for preprocessing and O((k+1)3m3) flopsfor iterations and is more proper for large-scale computations when m≪n. The convergence and complexity of the algorithm are subsequently analyzed. Illustrative numerical experiments indicate that the presented algorithm, which consists of a dominant time-consuming preprocessing step and a trivially iterative step, is capable of computing the solution efficiently for large-scale DAREs.
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