Volume 39, pp. 144-155, 2012.

Estimations of the trace of powers of positive self-adjoint operators by extrapolation of the moments

Claude Brezinski, Paraskevi Fika, and Marilena Mitrouli

Abstract

Let $A$ be a positive self-adjoint linear operator on a real separable Hilbert space $H$. Our aim is to build estimates of the trace of $A^q$, for $q\in \mathbb{R}$. These estimates are obtained by extrapolation of the moments of $A$. Applications of the matrix case are discussed, and numerical results are given.

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Key words

Trace, positive self-adjoint linear operator, symmetric matrix, matrix powers, matrix moments, extrapolation.

AMS subject classifications

65F15, 65F30, 65B05, 65C05, 65J10, 15A18, 15A45.

ETNA articles which cite this article

Vol. 43 (2014-2015), pp. 70-89 Paraskevi Fika, Marilena Mitrouli, and Paraskevi Roupa: Estimates for the bilinear form $x^T{A}^{-1}y$ with applications to linear algebra problems

Vol. 47 (2017), pp. 179-196 Marilena Mitrouli and Paraskevi Roupa: Vector estimates for f(A)b via extrapolation