83 research outputs found
Orthogonal Cauchy-like matrices
Cauchy-like matrices arise often as building blocks in decomposition formulas and fast algorithms for various displacement-structured matrices. A complete characterization for orthogonal Cauchy-like matrices is given here. In particular, we show that orthogonal Cauchy-like matrices correspond to eigenvector matrices of certain symmetric matrices related to the solution of secular equations. Moreover, the construction of orthogonal Cauchy-like matrices is related to that of orthogonal rational functions with variable poles
1-hypergroups of small sizes
In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation \u3b2. Many of these hypergroups can be obtained using the aforesaid hypergroup construction
Generalized modularity matrices
Various modularity matrices appeared in the recent literature on network
analysis and algebraic graph theory. Their purpose is to allow writing as
quadratic forms certain combinatorial functions appearing in the framework of
graph clustering problems. In this paper we put in evidence certain common
traits of various modularity matrices and shed light on their spectral
properties that are at the basis of various theoretical results and practical
spectral-type algorithms for community detection
Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
In this paper we will review the main results concerning the issue of
stability for the determination unknown boundary portion of a thermic
conducting body from Cauchy data for parabolic equations. We give detailed and
selfcontained proofs. We prove that such problems are severely ill-posed in the
sense that under a priori regularity assumptions on the unknown boundaries, up
to any finite order of differentiability, the continuous dependence of unknown
boundary from the measured data is, at best, of logarithmic type
ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS
International audienceWe study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data
Spectral properties of Hankel matrices and numerical solutions of finite moment problems
AbstractAfter proving that any Hankel matrix generated by moments of positive functions is conditioned essentially the same as the Hilbert matrix of the same size, we show a preconditioning technique, i.e., a congruence transform of the original Hankel matrix that drastically reduces its ill-conditioning. Applications of this result to classical orthogonal polynomial sequences and to modified moment problems are given. Also, we outline an efficient algorithm for the computation of the function f(x) = w(x) exp (p(x)), where w(x) is positive and p(x) is a polynomial of degree n−1, from the knowledge of its first n moments
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