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• W2034170049 abstract "In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$. We give explicit formulas for the banded approximations of $A^{-1}$ as well as bounds on their accuracy and speed of convergence in terms of their band-width. In the second part we apply these results to covariance matrices $Sigma$ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of $Sigma$. Finally, we note some applications of our results to statistics." @default.
• W2034170049 created "2016-06-24" @default.
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• W2034170049 date "2010-02-24" @default.
• W2034170049 modified "2023-09-27" @default.
• W2034170049 title "Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics" @default.
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