scholarly journals Matrix kernels for the Gaussian orthogonal and symplectic ensembles

2005 ◽  
Vol 55 (6) ◽  
pp. 2197-2207 ◽  
Author(s):  
Craig A. Tracy ◽  
Harold Widom
Keyword(s):  
Orthogonal And Symplectic Ensembles ◽  
Matrix Kernels

Spectral statistics of orthogonal and symplectic ensembles

2018 ◽  
Author(s):  
Greg W. Anderson
Keyword(s):  
Orthogonal Polynomials ◽  
Fundamental Theorem ◽  
The Other ◽  
Classical Orthogonal Polynomials ◽  
The Matrix ◽  
Spectral Statistics ◽  
Orthogonal And Symplectic Ensembles ◽  
The One ◽  
Gap Probabilities ◽  
Matrix Kernels

This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

scholarly journals OSKI: A library of automatically tuned sparse matrix kernels

2005 ◽  
Vol 16 ◽  
pp. 521-530 ◽  
Author(s):  
Richard Vuduc ◽  
James W Demmel ◽  
Katherine A Yelick
Keyword(s):  
Sparse Matrix ◽  
Matrix Kernels
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