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• W2100057277 abstract "This paper considers the solution of large-scale Lyapunov matrix equations of the form AX + XA <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>T</sup> = -bb <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>T</sup> . The Arnoldi method is a simple but sometimes ineffective approach to deal with such equations. One of its major drawbacks is excessive memory consumption caused by slow convergence. To overcome this disadvantage, we propose two-pass Krylov subspace methods, which only compute the solution of the compressed equation in the first pass. The second pass computes the product of the Krylov subspace basis with a low-rank approximation of this solution. For symmetric A, we employ the Lanczos method; for nonsymmetric A, we extend a recently developed restarted Arnoldi method for the approximation of matrix functions. Preliminary numerical experiments reveal that the resulting algorithms require significantly less memory at the expense of extra matrix-vector products." @default.
• W2100057277 created "2016-06-24" @default.
• W2100057277 creator A5084601962 @default.
• W2100057277 date "2008-01-01" @default.
• W2100057277 modified "2023-09-25" @default.
• W2100057277 title "Memory-efficient Krylov subspace techniques for solving large-scale Lyapunov equations" @default.
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• W2100057277 doi "https://doi.org/10.1109/cacsd.2008.4627370" @default.
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