We provide algorithms for computing the Karcher mean of positive definite semi-infinite quasi-Toeplitz matrices. After showing that the power mean of quasi-Toeplitz matrices is a quasi-Toeplitz matrix, we obtain a first algorithm based on the fact that the Karcher mean is the limit of a family of power means. A second algorithm, that is shown to be more effective, is based on a generalization to the infinite-dimensional case of a reliable algorithm for computing the Karcher mean in the finite-dimensional case. Numerical tests show that the Karcher mean of infinite-dimensional quasi-Toeplitz matrices can be effectively approximated with a finite number of parameters.

Algorithms for Approximating Means of Semi-infinite Quasi-Toeplitz Matrices

Iannazzo B.;
2021

Abstract

We provide algorithms for computing the Karcher mean of positive definite semi-infinite quasi-Toeplitz matrices. After showing that the power mean of quasi-Toeplitz matrices is a quasi-Toeplitz matrix, we obtain a first algorithm based on the fact that the Karcher mean is the limit of a family of power means. A second algorithm, that is shown to be more effective, is based on a generalization to the infinite-dimensional case of a reliable algorithm for computing the Karcher mean in the finite-dimensional case. Numerical tests show that the Karcher mean of infinite-dimensional quasi-Toeplitz matrices can be effectively approximated with a finite number of parameters.
2021
978-3-030-80208-0
978-3-030-80209-7
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1501221
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