Algorithms for Numerical Analysis in High Dimensions

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 f...

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Bibliographic Details
Published in:	SIAM journal on scientific computing Vol. 26; no. 6; pp. 2133 - 2159
Main Authors:	Beylkin, Gregory, Mohlenkamp, Martin J.
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2005
Subjects:	Accuracy Algorithms Applied mathematics Approximations and expansions Engineering Sciences Euclidean space Exact sciences and technology Linear algebra Mathematical analysis Mathematics Mechanics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical approximation Quantum physics Sciences and techniques of general use Structural mechanics separation-rank reduction separated representation Direct method Separation method 65Z05 Least squares method 41A63 Algorithm complexity Multidimensional operator 41A29 Dimensionality multiparticle Schrödinger equation curse of dimensionality Numerical linear algebra Antisymmetric function separated solutions of linear systems 65Y20 antisymmetric functions 65D15 Schrödinger equation 81-08 alternating least squares Numerical analysis Linear system Scientific computation Multidimensional space Matrix inversion Quantum mechanics Multidimensional function Condition number algorithms in high dimensions separation of variables Algorithm analysis multidimensional function antisymmetric functions multidimensional operator
ISSN:	1064-8275, 1095-7197
Online Access:	Get full text
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