Fast(er) linear algebra on multivariate Hankel matrices
Bernard Mourrain
AROMATH, Inria Sophia Antipolis Mediterranee
Date: 17 Noe 2016,
Time: 11:0012:00,
Room: 2600/101
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
submatrices.
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 BerlekampMasseySakata algorithm used in the decoding of ReedSolomon 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
Christoph Koutschan
Johann Radon Institute for
Computational and Applied Mathematics (RICAM), Linz
Austria
Date: 8 Noe 2016,
Time: 11:0012:00,
Room: 2526/105

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