Prediction and the Inverse of Toeplitz Matrices
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.
KeywordsToeplitz Operator Toeplitz Matrix Toeplitz Matrice Stationary Stochastic Process Displacement Rank
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