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Evaluating the action of a matrix function on a vector, that is x=f(M)v, is an ubiquitous task in applications. When M is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...
We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on the setting in wh ...
Institute of Electrical and Electronics Engineers2018
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...
The minimal faithful permutation degree (G) of a finite group G is the least nonnegative integer n such that G embeds in the symmetric group Sym(n). Clearly (G x H) (G) + (H) for all finite groups G and H. In 1975, Wright ([10]) proved that equality occurs ...
We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift (2j)ω+jy+xmod1 for irrational ω. We prove that the eigenvalue distribution of these matrices conv ...
Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let be the subgroup of generated by the elementary matrices. In this paper we study the action of by matrix multiplication on the set of unimodular r ...
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retai ...
Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...
The problem of finding a k×k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...
