# Prediction and the Inverse of Toeplitz Matrices

• I. Gohberg
• H. J. Landau
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)

## Abstract

Toeplitz matrices represent the discrete analogue of convolutions, and the problem of inverting them is often encountered. The inverse of a Toeplitz matrix is no longer Toeplitz. However, thanks to a formula of Gohberg and Semençul, it can be expressed in terms of two closely related triangular Toeplitz matrices. Here we use an analogy with predicting stationary stochastic processes to motivate a simple proof of this formula, as well as of the main facts in the classical trigonometric moment problem.

## Keywords

Toeplitz Operator Toeplitz Matrix Toeplitz Matrice Stationary Stochastic Process Displacement Rank
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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