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Block locally Toeplitz sequences: construction and properties. (English) Zbl 1445.15004

Bini, Dario Andrea (ed.) et al., Structured matrices in numerical linear algebra. Analysis, algorithms and applications. Selected papers of the INdAM meeting on structured matrices in numerical linear algebra: analysis, algorithms and applications, Cortona, Italy, September 4–8, 2017. Cham: Springer. Springer INdAM Ser. 30, 25-58 (2019).
Summary: The theory of block locally Toeplitz (LT) sequences – along with its generalization known as the theory of block generalized locally Toeplitz (GLT) sequences – is a powerful apparatus for computing the spectral distribution of matrices arising from the discretization of differential problems. In this paper we develop the theory of block LT sequences, whereas the theory of block GLT sequences is the subject of the complementary paper (Chap. 3 of this book).
For the entire collection see [Zbl 1416.65008].

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B05 Toeplitz, Cauchy, and related matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B57 Hermitian, skew-Hermitian, and related matrices
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