The efficient computation of scalar products of certain antisymmetric functions

Wolfgang Hackbusch

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Submission date: 01. Mar. 2000
Pages: 14
published in: Computing, 67 (2001) 1, p. 35-56 
DOI number (of the published article): 10.1007/s006070170015
Bibtex
with the following different title: The efficient computation of certain determinants arising in the treatment of Schrödinger's equations
MSC-Numbers: 65F40, 81-08
Keywords and phrases: schrödinger equation, antisymmetric functions, sparse grids, evaluation of scalar products
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Abstract:
The solution of Schrödinger's equation leads to a high number N of independent variables. Furthermore, the restriction to (anti)symmetric functions implies some complications. We propose a sparse-grid approximation which leads to a set of non-orthogonal basis. Due to the antisymmetry, scalar products are expressed by sums of -determinants. More precisely, we have to determine

where are entries of the K matrices in We propose a method to evaluate this expression such that the computational cost amounts to for fixed K, while the storage requirements are