Abstract
AbstractIt is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$
f
, appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$
f
is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$
f
. The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$
f
is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$
f
. Future research directions are outlined at the end of the paper.
Funder
Athens University of Economics and Business
Vetenskapsrådet
Uppsala University
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献