Caterina Fenu

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Approximations of matrix-valued functions of the form WT f(A)W , where A ∈ Rm×m is symmetric, W ∈ Rm×k , with m large and k m, has orthonormal columns, and f is a function, can be computed by applying a few steps of the symmetric block Lanczos method to A with initial block-vector W ∈ Rm×k . Golub and Meurant have shown that the approximants obtained in(More)
Large-scale networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to ascertain the ease of traveling between nodes. These and related quantities can be determined by evaluating expressions of the form uT f(A)w, where A is the adjacency matrix that represents the graph of the network, f(More)
Large-scale networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to determine the ease of traveling between them. We are interested in carrying out these tasks for directed networks. These networks have a nonsymmetric adjacency matrix A. Benzi et al. [6] recently proposed that these(More)
Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of adjacency matrices. We consider here the issue of representing the system as a single, higher dimensional block(More)
Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on(More)
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are(More)
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