Sequences of Structured Matrices: Tools and Applications - Brossura

Sesana, Debora; Serra Capizzano, Stefano

 
9783659162428: Sequences of Structured Matrices: Tools and Applications

Sinossi

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.

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L'autore

Debora Sesana received the PhD in Applied Mathematics in 2011. She is a postdoctoral fellow at the SEI Department, University of Piemonte Orientale - Novara. Stefano Serra Capizzano received the PhD in Applied Mathematics and Optimisation in 1996. He is Dean of the Faculty of Sciences at the Insubria University - Como.

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