• Publications
  • Influence
IEEE Standard for Floating-Point Arithmetic
  • 1,090
  • 50
The efficient evaluation of the hypergeometric function of a matrix argument
TLDR
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions, using the combinatorial properties of the Jack function. Expand
  • 223
  • 35
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Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
  • P. Koev
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1 May 2005
TLDR
We present new O(n3) algorithms that, given the bidiagonal factors of a nonsingular TN matrix, compute its eigenvalues and SVD to high relative accuracy in floating point arithmetic, independent of the conventional condition number. Expand
  • 95
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On the largest principal angle between random subspaces
Formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p-dirnensional subspaces of R-n chosen from the uniformExpand
  • 68
  • 10
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Accurate Computations with Totally Nonnegative Matrices
  • P. Koev
  • Computer Science, Mathematics
  • SIAM J. Matrix Anal. Appl.
  • 1 October 2007
TLDR
We consider the problem of performing accurate computations with rectangular $(m\times n)$ totally nonnegative matrices. Expand
  • 77
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The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System
  • J. Demmel, P. Koev
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1 May 2005
TLDR
We prove that Bjorck--Pereyra-type methods exist not only for the above linear systems but also for any totally positive linear system as long as the initial minors (i.e., contiguous minors that include the first row or column) can be computed accurately. Expand
  • 93
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Accurate SVDs of weakly diagonally dominant M-matrices
TLDR
We present a new O(n3) algorithm which computes the SVD of a weakly diagonally dominant M-matrix to high relative accuracy. Expand
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  • 4
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Implicit standard Jacobi gives high relative accuracy
TLDR
We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDXT of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. Expand
  • 26
  • 4
Distributions of the Extreme Eigenvaluesof Beta-Jacobi Random Matrices
TLDR
We present explicit formulas for the distributions of the extreme eigenvalues of the $\beta$-Jacobi random matrix ensemble in terms of the hypergeometric function of a matrix argument. Expand
  • 35
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Accurate and efficient expression evaluation and linear algebra
TLDR
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. Expand
  • 36
  • 2
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