求解具有高秩常數項的大型代數黎卡迪方程式之數值方法

In this proposal, we consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We plan to modify the doubling algorithm, making use of the low-rank in the input matrix $B$. We will also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Finally, illustrative numerical examples will be presented for demonstrating the effectiveness and feasibility of the proposed algorithms.