Convergence analysis of the extended Krylov subspace method for the Lyapunov equation

Authors:
L. Knizhnerman;V. Simoncini
Affiliations:
Central Geophysical Expedition, house 38, building 3, Narodnogo opolcheniya St., 123298, Moscow, Russia;Dipartimento di Matematica, CIRSA, Università di Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Ravenna, Italy
Venue:
Numerische Mathematik
Year:
2011

Citing 0
Cited 3

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Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation

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An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation

SIAM Journal on Numerical Analysis

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Abstract

The extended Krylov subspace method has recently arisen as a competitive method for solving large-scale Lyapunov equations. Using the theoretical framework of orthogonal rational functions, in this paper we provide a general a priori error estimate when the known term has rank-one. Special cases, such as symmetric coefficient matrix, are also treated. Numerical experiments confirm the proved theoretical assertions.