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math.CA2012★ 22 cited
Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
N. S. Witte, F. Bornemann, P. J. Forrester
The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlevé II transcendent and its as…
math.NA2012★ 2 cited
Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlevé II Transcendents
Georg Wechslberger, Folkmar Bornemann
The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular…
math.NA2012
On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity
Shuhuang Xiang, Folkmar Bornemann
We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw-Curtis when applied to functions of limited regularity: if the Chebyshev coef…