Singular Value and Eigenvalue Distribution of a Matrix-Sequence

Carlo Garoni () and Stefano Serra-Capizzano ()
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Carlo Garoni: University of Insubria, Department of Science and High Technology
Stefano Serra-Capizzano: University of Insubria, Department of Science and High Technology

Chapter Chapter 3 in Generalized Locally Toeplitz Sequences: Theory and Applications, 2017, pp 45-55 from Springer

Abstract: Abstract Throughout this book, a matrix-sequence (or sequence of matrices) is any sequence of the form $$\{A_n\}_n$$ , where $$A_n\in \mathbb C^{n\times n}$$ and n varies in some infinite subset of $$\mathbb N$$ . This chapter introduces the notion of (asymptotic) singular value and eigenvalue distribution for a matrix-sequence, as well as other related concepts such as clustering and attraction. A special attention is devoted to the so-called zero-distributed sequences, which play a central role in the theory of GLT sequences.

Keywords: Matrix Sequence; Eigenvalue Distribution; Singular Value; Toeplitz Matrices; Diagonal Sampling (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-53679-8_3

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