کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423161 | 1341255 | 2012 | 22 صفحه PDF | دانلود رایگان |
For a given nonnegative integer g, a matrix An of size n is called g-Toeplitz if its entries obey the rule An=[arâgs]r,s=0nâ1. Analogously, a matrix An again of size n is called g-circulant if An=[a(râgs)modn]r,s=0nâ1. In a recent work we studied the asymptotic properties, in terms of spectral distribution, of both g-circulant and g-Toeplitz sequences in the case where {ak} can be interpreted as the sequence of Fourier coefficients of an integrable function f over the domain (âÏ,Ï). Here we are interested in the preconditioning problem which is well understood and widely studied in the last three decades in the classical Toeplitz case, i.e., for g=1. In particular, we consider the generalized case with gâ¥2 and the nontrivial result is that the preconditioned sequence {Pn}={Pnâ1An}, where {Pn} is the sequence of preconditioner, cannot be clustered at 1 so that the case of g=1 is exceptional. However, while a standard preconditioning cannot be achieved, the result has a potential positive implication since there exist choices of g-circulant sequences which can be used as basic preconditioning sequences for the corresponding g-Toeplitz structures. Generalizations to the block and multilevel case are also considered, where g is a vector with nonnegative integer entries. A few numerical experiments, related to a specific application in signal restoration, are presented and critically discussed.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 8, February 2012, Pages 2090-2111