We derive upper bounds for the 2-condition number of H as functions of n, r l and z l, which show that the Hankel matrix H becomes well conditioned whenever the z's are close to the unit circle but not extremely close to each other. Numerical results which illustrate the theory are ...
Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed...
C. Lay, Factorization of finite rank Hankel and Toeplitz matrices, Linear Algebra Appl., 173 (1992), 19-38.R.L. Ellis and D.C. Lay, "Factorization of finite rank Hankel and Toeplitz matrices," Linear algebra and its applications, vol. 173, pp. 19-38, 1992....
We present a new algorithm for the decomposition of a multivariate Hankel matrix Ho. as a sum of Hankel matrices of small rank. This decomposition corresponds to the decomposition of its symbol sigma as a sum of polynomial-exponential series. By exploiting the properties of the associated Artini...
Infinite Hankel matrices of finite rankGeneralized Fibonacci sequenceGenerating and representing measureHamburger moment problemZ-transformIn this paper, we propose an approach that utilizes the generalized Fibonacci sequence as a tool for studying the infinite Hankel matrix of finite rank, associated with ...
I delivered a similar paper at the 2015 SEG annual convention entitled 'Preserving signal: Automatic rank determination for noise suppression' (Trickett, 2015), which I will refer to as T15. Here I discuss some of the similarities and differences between the two papers....
extended field of operator theoryG. Heinig, K. Rost, Fast “split” algorithms for Toeplitz and Toeplitz-plus-Hankel matrices with arbitrary rank profile. Proceedings of the International Conference on Mathematics and its Applications (ICMA 2004), 285–312, Kuwait, 2005....
We present a new algorithm for the decomposition oJ. Harmouch a bH. Khalil bB. Mourrain aLinear Algebra and its ApplicationsJ. Harmouch, H. Khalil, and B. Mourrain, Structured Low Rank Decomposition of Multi- variate Hankel Matrices, hal-01440063, (2017)....
Rank-1 Hankel and Toeplitz matricesCadzow algorithmWe characterize optimal rank-1 matrix approximations with Hankel or Toeplitz structure with regard to two different norms, the Frobenius norm and the spectral norm, in a new way. More precisely, we show that these rank-1 matrix approximation ...
In this review, we summarize the recent progress on low rank Hankel matrix and tensor methods, that exploit the exponential property of free induction decay signals, to enable effective denoising and spectra reconstruction. We also outline future developments that are likely to make NMR spectroscopy ...