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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 u T f (A)w, where A is the adjacency matrix that represents the graph of the network, f… (More)

Approximations of matrix-valued functions of the form W T f (A)W , where A ∈ R m×m is symmetric, W ∈ R m×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 ∈ R m×k. Golub and Meurant have shown that the approximants obtained in… (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)

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing… (More)

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