This book provides a systematic and unifying treatment of the
spectral analysis of matrix sequences collecting the state of the
art of the research in this field and providing new advanced
results which are interesting both from the theoretical and from
the algorithmic point of view. The first part concerns the
description and analysis of the available tools, together with
their generalization including the development of new effective
tools of analysis. The basic concept of "approximating class of
sequences" is introduced and analyzed in depth. Some new results of
great interest have been obtained and applied to Toeplitz
sequences. The classes of g-circulant and g-Toeplitz matrix
sequences are introduced as well, and their spectral analysis is
carried out. The second part is addressed to applications. It
contains new and interesting results. A relevant role is played by
the preconditioning of g-Toeplitz matrix sequences by means of
g-circulant matrices with a specific attention to the regularizing
properties which take their importance in the applications
concerning image processing, filtering and restoration. Another
application concerns two-grid and multi-grid techniques.
General
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