منابع مشابه
The smallest eigenvalue of Hankel matrices
Let HN = (sn+m), n,m ≤ N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue λN of HN . It is proved that λN has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of λN can be arbitrarily slow or arbitrarily fast. In the indeterminate ca...
متن کاملComputing the smallest eigenvalue of large ill-conditioned Hankel matrices
This paper presents a parallel algorithm for finding the smallest eigenvalue of a particular form of ill-conditioned Hankel matrix, which requires the use of extremely high precision arithmetic. Surprisingly, we find that commonly-used approaches that are designed for high efficiency are actually less efficient than a direct approach under these conditions. We then develop a parallel implementa...
متن کاملSmallest Eigenvalues of Hankel Matrices for Exponential Weights
We obtain the rate of decay of the smallest eigenvalue of the Hankel matrices R I t j+kW 2 (t) dt n j;k=0 for a general class of even exponential weights W 2 = exp ( 2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors. Remark 1 Running Title: Smallest Eigenvalues of Hankel Matrices
متن کاملFinding the Smallest Eigenvalue by Properties of Semidefinite Matrices
We consider the smallest eigenvalue problem for symmetric or Hermitian matrices by properties of semidefinite matrices. The work is based on a floating-point Cholesky decomposition and takes into account all possible computational and rounding errors. A computational test is given to verify that a given symmetric or Hermitian matrix is not positive semidefinite, so it has at least one negative ...
متن کاملOn the Smallest Eigenvalue of General correlated Gaussian Matrices
Abstract—This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. This work is, in particular, motivated by applications from statistical signal proce...
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2010
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-010-9109-4