Explicit inverse of tridiagonal matrix with applications in autoregressive modelling

Autor:	Linda S. L. Tan
Rok vydání:	2019
Předmět:	Tridiagonal matrix Autoregressive model Applied Mathematics 0211 other engineering and technologies Applied mathematics Inverse 021107 urban & regional planning 02 engineering and technology 010501 environmental sciences 01 natural sciences 0105 earth and related environmental sciences Mathematics
Zdroj:	IMA Journal of Applied Mathematics.
ISSN:	1464-3634 0272-4960
Popis:	We present the explicit inverse of a class of symmetric tridiagonal matrices, which is almost Toeplitz, except that the first and last diagonal elements are different from the rest. This class of tridiagonal matrices is of special interest in complex statistical models, which uses the first-order autoregression to induce dependence in the covariance structure, for instance, in econometrics or spatial modelling. They also arise in interpolation problems using the cubic spline. We show that the inverse can be expressed as a linear combination of Chebyshev polynomials of the second kind and present results on the properties of the inverse, such as bounds on the row sums, the trace of the inverse and its square and their limits as the order of the matrix increases.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d69f1d20169c937c184effc29b09c851 https://doi.org/10.1093/imamat/hxz010 Zobrazit plný text záznamu