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.
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Dedicated to Walter Gautschi on his 65th birthday
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© 1994 Birkhäuser
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Gohberg, I., Landau, H.J. (1994). Prediction and the Inverse of Toeplitz Matrices. In: Zahar, R.V.M. (eds) Approximation and Computation: A Festschrift in Honor of Walter Gautschi. ISNM International Series of Numerical Mathematics, vol 119. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-7415-2_14
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DOI: https://doi.org/10.1007/978-1-4684-7415-2_14
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