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Moments of a linear operator, with applications to the trace of the inverse of matrices and the solution of equations
Author(s) -
Brezinski Claude,
Fika Paraskevi,
Mitrouli Marilena
Publication year - 2012
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.803
Subject(s) - mathematics , invertible matrix , hilbert space , trace (psycholinguistics) , extrapolation , inverse , operator (biology) , norm (philosophy) , linear operators , linear map , mathematical analysis , trace class , algebra over a field , pure mathematics , philosophy , linguistics , biochemistry , geometry , chemistry , repressor , political science , transcription factor , law , bounded function , gene
SUMMARY Let H be a real finite dimensional Hilbert space and A an invertible linear operator on it. In this paper, we are interested in obtaining estimations of Tr ( A −1 ) and of the norm of the error when solving the equation Ax = f ∈ H . These estimates are obtained by extrapolation of the moments of A . Numerical results are given, and applications are discussed. Copyright © 2011 John Wiley & Sons, Ltd.