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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2005

Algorithms for Numerical Analysis in High Dimensions

Résumé

Nearly every numerical analysis algorithm has computational complexity that scales exponentially in the underlying physical dimension. The separated representation, introduced previously , allows many operations to be performed with scaling that is formally linear in the dimension. In this paper we further develop this representation by (i) discussing the variety of mechanisms that allow it to be surprisingly efficient; (ii) addressing the issue of conditioning; (iii) presenting algorithms for solving linear systems within this framework; and (iv) demonstrating methods for dealing with antisymmetric functions, as arise in the multiparticle Schrödinger equation in quantum mechanics. Numerical examples are given.
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Dates et versions

hal-02076682 , version 1 (22-03-2019)

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Gregory Beylkin, Martin Mohlenkamp. Algorithms for Numerical Analysis in High Dimensions. SIAM Journal on Scientific Computing, 2005, 26 (6), pp.2133-2159. ⟨10.1137/040604959⟩. ⟨hal-02076682⟩

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