Extrapolation Methods for Estimating the Trace of the Matrix Inverse

Paraskevi Fika ()
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Paraskevi Fika: National and Kapodistrian University of Athens

A chapter in Modern Discrete Mathematics and Analysis, 2018, pp 173-185 from Springer

Abstract: Abstract The evaluation of the trace of the matrix inverse, Tr(A −1), arises in many applications and an efficient approximation of it without evaluating explicitly the matrix A −1 is very important, especially for large matrices that appear in real applications. In this work, we compare and analyze the performance of two numerical methods for the estimation of the trace of the matrix A −1, where A ∈ ℝ p × p $$A \in {\mathbb {R}}^{p \times p}$$ is a symmetric matrix. The applied numerical methods are based on extrapolation techniques and can be adjusted for the trace estimation either through a stochastic approach or via the diagonal approximation. Numerical examples illustrating the performance of these methods are presented and a useful application of them in problems stemming from real-world networks is discussed. Through the presented numerical results, the methods are compared in terms of accuracy and efficiency.

Keywords: Trace; Matrix inverse; Extrapolation; Prediction; Aitken’s process; Moments (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-74325-7_7

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DOI: 10.1007/978-3-319-74325-7_7

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