查看更多>>摘要：Spectral projectors of Hermitian matrices play a key role in many applications, such as electronic structure computations. Linear scaling methods for gapped systems are based on the fact that these special matrix functions are localized, which means that the entries decay rapidly away from the main diagonal or with respect to more general sparsity patterns. The relation with the sign function together with an integral representation is used to obtain new decay bounds, which turn out to be optimal in an asymptotic sense. The influence of isolated extremal eigenvalues on the decay properties is also investigated and a superexponential behaviour is predicted.
查看更多>>摘要：This paper provides an accurate method to obtain the bidiagonal factorization of Wronskian matrices of Bessel polynomials and of Laguerre polynomials. This method can be used to compute with high relative accuracy their singular values, the inverse of these matrices, as well as the solution of some related systems of linear equations. Numerical examples illustrating the theoretical results are included.
查看更多>>摘要：This paper discusses the convexity of the range of the Berezin transform. For a bounded operator T acting on a reproducing kernel Hilbert space H (on a set X), this is the set B(T):={〈Tk?x,k?x〉H:x∈X}, where k?x is the normalized reproducing kernel for H at x∈X. Primarily, we focus on characterizing convexity of this range for a class of composition operators acting on the Hardy space of the unit disk.
查看更多>>摘要：In this article, we introduce a new matrix class Lˉ(d) (a subclass of Q0-matrices which are obtained as a limit of a sequence of L(d)-matrices) such that for any A in this class, a solution to LCP(q,A) exists if LCP(q,A) is feasible, and Lemke's algorithm will find a solution or demonstrate infeasibility. We present a counterexample to show that an Lˉ(d)-matrix need not be an L(d)-matrix. We also show that if A∈Lˉ(d), there is an even number of solutions for any nondegenerate vector q. An application of this new matrix class that arises from general quadratic programs and polymatrix games belongs to this class. Finally, we present an example related to the existence of equilibrium in polymatrix games.
查看更多>>摘要：In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra sl(2,C) and the form for these characteristic polynomials, and prove there is one to one correspondence between representations and their characteristic polynomials. Moreover we define a monoid structure on these characteristic polynomials.
查看更多>>摘要：We construct a new family of linearizations of rational matrices R(λ) written in the general form R(λ)=D(λ)+C(λ)A(λ)?1B(λ), where D(λ), C(λ), B(λ) and A(λ) are polynomial matrices. Such representation always exists and is not unique. The new linearizations are constructed from linearizations of the polynomial matrices D(λ) and A(λ), where each of them can be represented in terms of any polynomial basis. In addition, we show how to recover eigenvectors, when R(λ) is regular, and minimal bases and minimal indices, when R(λ) is singular, from those of their linearizations in this family.
查看更多>>摘要：A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with the Empirical Mode Decomposition (EMD) and its more rigorous mathematical structure, which makes feasible to study its convergence compared to EMD, ALIF has really good potentiality to become a reference method in the analysis of signals containing strong nonstationary components, like chirps, multipaths and whistles, in many applications, like Physics, Engineering, Medicine and Finance, to name a few. In [9], the authors analyzed the spectral properties of the matrices produced by the ALIF method, in order to study its stability. Various results are achieved in that work through the use of Generalized Locally Toeplitz (GLT) sequences theory, a powerful tool originally designed to extract information on the asymptotic behavior of the spectra for PDE discretization matrices. In this manuscript we focus on answering some of the open questions contained in [9], and in doing so, we also develop new theory and results for the GLT sequences.
NSTL
Elsevier