Relaxing order basis computation

Pascal Giorgi 1 Romain Lebreton 1, 2
1 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The computation of an order basis (also called sigma basis) is a fundamental tool for linear algebra with polynomial coefficients. Such a computation is one of the key ingredients to provide algorithms which reduce to polynomial matrices multiplication. This has been the case for column reduction or minimal nullspace basis of polynomial matrix over a field. In this poster, we are interested in the application of order basis to compute minimal matrix generators of a linear matrix sequence. In particular, we focus on the linear matrix sequence used in the Block Wiedemann algorithm.
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Pascal Giorgi, Romain Lebreton. Relaxing order basis computation. ACM Communications in Computer Algebra, Association for Computing Machinery (ACM), 2014, 47 (3/4), pp.100-101. ⟨10.1145/2576802.2576813⟩. ⟨lirmm-01372532⟩

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