## 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.

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