A Structure Preserving FGMRES Method for Solving Large Lyapunov Equations

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “• the conjugate gradient method, BiCGStab and other Krylov subspace methods combined with HT [170, 172, 248] and low-rank matrix decompositions [33];”
Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey (2013, background): “Eppler and Bollhöfer in a series of conference papers derived a flexible generalized minimal residual (FGMRES) type iteration with ADI preconditioning [15].”
Computational Methods for Linear Matrix Equations (2016, methodology): “More recently, a flexible GMRES approach was proposed in [46], which allowed for a variable ADI preconditioning step.”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, background): “…exploit the low-rank property particularly for the solution of large-scale, sparse Lyapunov equations, see, e.g., – Krylov subspace methods [64,69,70,113,115,116,118, 120,138,172,180,181],andtensorKrylovsubspacemeth-ods [31,126], – the factorized sign function iteration [34,43,44], and…”
On two numerical methods for the solution of large-scale algebraic Riccati equations (2014, unknown): “, [2], [22], [28], [47] and references therein.”