Fast(er) linear algebra on multivariate Hankel matrices
AROMATH, Inria Sophia Antipolis Mediterranee
Date: 17 Noe 2016, Time: 11:00-12:00, Room: 26-00/101
Hankel operators and matrices occur in many problems, such as sparse interpolation, representation of functions as sums of exponentials, tensor decomposition, quadrature formulae, recurrence relations of sequences, algebraic code decoding... These applications often require to compute kernels of Hankel matrices and eigenvectors of some sub-matrices.
We give some properties of these Hankel matrices in the multivariate case, which are related to their decomposition as sum of Hankel matrices of small rank. We present a fast algorithm to compute the kernel of such matrices, which compares favorably with Berlekamp-Massey-Sakata algorithm used in the decoding of Reed-Solomon codes by syndrome. We describe how to deduce a decomposition of these multivariate Hankel matrices, that accelerate some linear algebra operations. Some examples of applications will illustrate these methods.
Symbolic Determinants support Numerical Methods
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz Austria
Date: 8 Noe 2016, Time: 11:00-12:00, Room: 25-26/105