[PDF] Top 20 Solving Large-Scale Continuous-Time Algebraic Riccati Equations by Doubling

... Lyapunov equations as well as periodic systems, implementation on GPUs and other parallel computing platforms, associated compu- tation of controllability and observability Gramians and balanced truncation methods ... See full document

... Example 1 The cooling of steel profile example is quoted from [29], with n = 1357 , m = 7 , l = 6. From Table 4, the accuracy of O ( 10 − 16 ) , better than those in [34,11], is achieved within seven iterations, in 2.55 ... See full document

... Lin, Solving large-scale discrete-time algebraic Riccati equations by doubling, Technical Re- port, NCTS Preprints in Mathematics, 2012-5-002, National Tsing ... See full document

... to large-scale CAREs, Stein and Lyapunov equations as well as periodic systems, implementation on GPUs and other parallel computing platforms, associated computation of controllability and ... See full document

... (1) The appropriate application of the Sherman-Morrison-Woodbury formula in order avoid the inversion of large matrices. (2) The use of sparse-plus-low-rank matrices. (3) The computation of matrix operators ... See full document

... SOLVING LARGE-SCALE NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS BY DOUBLING ∗ TIEXIANG LI † , ERIC KING-WAH CHU ‡ , YUEH-CHENG KUO § , AND WEN-WEI LIN ¶ ...the ... See full document

... Re ent developments and better understanding of doubling algorithms, espe ially the stru ture-preserving properties and eÆ ien y of the SDA [24℄, give this old approa h a new lease of life. In addition, we have ... See full document

... of large-scale Lyapunov and Stein equations with numerically low-ranked ...Stein equations, the structure-preserving doubling algorithm will be adapted, with the iterates for A not ... See full document

... g 22 = Y 2 T B k B k T Y 2 ≈ N r T B k B k T N r ≥ σ 2 (B k ) ≥ σ 2 (B 0 ), h 22 = X 2 T C k C k T X 2 ≈ N ` T C k C k T N ` ≥ σ 2 (C k ) ≥ σ 2 (C 0 ). Thus the partial measures for stabilizability and detectability are ... See full document

... structured doubling algorithm for solving the stabilizing or almost stabilizing solution of DARE ...computed by SDA is the same as the maximal solution computed by Newton’s ...structured ... See full document

... OF ALGEBRAIC RICCATI EQUATIONS TSUNG-MIN HWANG AND WEN-WEI LIN ...structured doubling algorithms for the computation of weak Hermitian solutions of continuous/discrete-time ... See full document

... OF ALGEBRAIC RICCATI EQUATIONS TSUNG-MIN HWANG AND WEN-WEI LIN ...structured doubling algorithms for the computation of weak Hermitian solutions of continuous/discrete-time ... See full document

... the large-scale problems we are interested in ...of large linear systems, large-scale CAREs, DAREs, Lyapunov and Stein equations have to be solved; see [2]–[9], [15]–[21], [23, ... See full document

... and large-scale Stein and Lyapunov equations, in our SDA ls for NAREs, the convergence of the doubling iteration competes with the exponential growth in B ik and C ik ...controlled by ... See full document

... the continuous-time case, a well-known backward stable algorithm care , proposed by [24], computes a Hermitian solution X for CARE by ap- plying QR algorithm to H with reordering ...proposed ... See full document

... of large-scale Lyapunov and Stein equa- tions. For Stein equations, the well-known Smith method will be adapted, with A k = A 2 k not explicitly computed but in the recursive form A k = A 2 k−1 , and ... See full document

... and let A = trid(20, −10, −10) ∈ R n×n , R = I n . The control matrix B and output matrix C are randomly generated with entries distributed normally in [ −1, 1]. We set rank(B) = rank(C) = ⌈ n 2 ⌉. Note that the matrix E ... See full document

... structure-preserving doubling algorithm (SDA) for computing the minimal nonnegative solutions to the nonsymmetric algebraic Riccati equation (NARE) based on the techniques developed in the symmetric ... See full document

... FPIs making them more expensive than NM (see examples in [9]). Recently, a structured doubling algorithm (SDA) has been developed in [11] for solving minimal nonnegative solutions X and Y of NARE (1.1) and ... See full document

... Hence, some Lanczos-type algorithms were proposed in [10-12] for computing large sparse Hamiltonian eigenvalue problems, in which the nonsym- metric look-ahead Lanczos [r] ... See full document