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The efficient evaluation of the hypergeometric function of a matrix argument


Authors: Plamen Koev and Alan Edelman
Journal: Math. Comp. 75 (2006), 833-846
MSC (2000): Primary 33C20, 65B10; Secondary 05A99
DOI: https://doi.org/10.1090/S0025-5718-06-01824-2
Published electronically: January 19, 2006
MathSciNet review: 2196994
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Abstract: We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.

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Additional Information

Plamen Koev
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: plamen@math.mit.edu

Alan Edelman
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: edelman@math.mit.edu

DOI: https://doi.org/10.1090/S0025-5718-06-01824-2
Keywords: Hypergeometric function of a matrix argument, Jack function, zonal polynomial, eigenvalues of random matrices
Received by editor(s): September 16, 2004
Received by editor(s) in revised form: February 26, 2005
Published electronically: January 19, 2006
Additional Notes: This work was supported in part by NSF Grant DMS-0314286.
Article copyright: © Copyright 2006 American Mathematical Society