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

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

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 uniform… Expand

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

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

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

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