文件名称:ALGORITHMS-FOR-NUMERICAL-ANALYSIS-IN-HIGH-DIMENSI
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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 ecient (ii) addressing the issue of conditioning
(iii) presenting algorithms for solving linear systems within this fr a mework and (iv) demonstrating methods for dealing
with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics. Numerical
examples are given.-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 ecient (ii) addressing the issue of conditioning
(iii) presenting algorithms for solving linear systems within this fr a mework and (iv) demonstrating methods for dealing
with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics. Numerical
examples are given.
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 ecient (ii) addressing the issue of conditioning
(iii) presenting algorithms for solving linear systems within this fr a mework and (iv) demonstrating methods for dealing
with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics. Numerical
examples are given.-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 ecient (ii) addressing the issue of conditioning
(iii) presenting algorithms for solving linear systems within this fr a mework and (iv) demonstrating methods for dealing
with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics. Numerical
examples are given.
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ALGORITHMS FOR NUMERICAL ANALYSIS IN HIGH DIMENSIONS.pdf