Finite sections method for Hessenberg matrices

Authors:
Leonel Robert;Luis Santiago
Affiliations:
Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Canada M5S 3G3;Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, Cuba CP 10400
Venue:
Journal of Approximation Theory
Year:
2003

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Abstract

Let D be a Hessenberg matrix and D the closed operator associated to it. In this work, we study the approximation of the resolvent of D by the resolvents of the truncated matrices Dn of D. A concept of determinacy is introduced analogous to the one for Jacobi matrices. We apply our results to some questions in rational approximation.