On the Parameter Selection Problem in the Newton-ADI Iteration for Large Scale Riccati Equations

By Peter Benner, Hermann Mena, Jens Saak. 2007

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Towards an ADI iteration for Tensor Structured Equations (2014, methodology): “The contribution in [7] combines the optimality of the Wachspress parameters and the fast computability of Penzl’s parameters.”
Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations (2014, methodology): “We also plan to adapt the proposed approaches to low-rank Newton-ADI methods [8, 10, 11, 13] for solving algebraic Riccati equations.”
AN EXTENDED BLOCK ARNOLDI ALGORITHM FOR LARGE-SCALE SOLUTIONS OF THE CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATI ON ∗ (2008, methodology): “The obtained results are compared with those obtained by the block Arnoldi Riccati method [17, 18] and by the NewtonADI method, also called the Low Rank Cholesky Factorized Newton (LRCF-Newton) method [8, 28].”
A preconditioned low‐rank CG method for parameter‐dependent Lyapunov matrix equations (2014, background): “Iteration number k α ∈ [1, 10], m = 10 α ∈ [1, 10], m = 100 α ∈ [1, 10], m ≈ 1e3 α ∈ [1, 10], m ≈ 1e4 α ∈ [1, 30], m = 30 α ∈ [1,100], m = 100”