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Conference Papers Year : 2023

Exact computations with quasiseparable matrices

Abstract

Quasi-separable matrices are a class of rank-structured matrices widely used in numerical linear algebra and of growing interest in computer algebra, with applications in e.g. the linearization of polynomial matrices. Various representation formats exist for these matrices that have rarely been compared. We show how the most central formats SSS and HSS can be adapted to symbolic computation, where the exact rank replaces threshold based numerical ranks. We clarify their links and compare them with the Bruhat format. To this end, we state their space and time cost estimates based on fast matrix multiplication, and compare them, with their leading constants. The comparison is supported by software experiments. We make further progresses for the Bruhat format, for which we give a generation algorithm, following a Crout elimination scheme, which specializes into fast algorithms for the construction from a sparse matrix or from the sum of Bruhat representations.
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Dates and versions

hal-03978799 , version 1 (08-02-2023)

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Clément Pernet, Hippolyte Signargout, Gilles Villard. Exact computations with quasiseparable matrices. ISSAC'23: the 2023 International Symposium on Symbolic and Algebraic Computation, Jul 2023, Tromso, Norway. pp.480-489, ⟨10.1145/2930889.2930915⟩. ⟨hal-03978799⟩
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