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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. [ABSTRACT FROM AUTHOR]

Study of Padé-Faber approximation (generalization of Padéapproximation and Padé-Chebyshev approximation) of Markov functions is important not only from the point of view of mathematical analysis, but also of computational mathematics. The theorem on the existence of subdiagonal approximants is constructively proved. Various estimates of the approximation error are given. Theoretical assertions are illustrated by simulation results. [ABSTRACT FROM AUTHOR]