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# Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics

Publikationstyp

Journal Article

Publikationsdatum

2012-05-28

Sprache

English

Enthalten in

Volume

56

Issue

1

Start Page

1

End Page

20

Citation

Theory of Probability and its Applications 56 (1): 1-20 (2012-05-28)

Publisher DOI

Scopus ID

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 ℓ 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 bandwidth. We then use these results to prove that the so-called Wiener algebra is inverse closed. In the second part of the paper we apply these results to covariance matrices ∑ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of ∑. Finally, we note some applications of our results to statistics. © by SIAM.