We consider the Givens QR factorization of banded Hessenberg-Toeplitz matrices of large order and relatively small bandwidth. We investigate the asymptotic behavior of the R factor and the Givens rotation when the order of the matrix goes to infinity, and present some interesting convergence properties. These properties can lead to savings in the computation of the exact QR factorization and gi...

We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with C∞-smooth, compactly supported basis functions in time and piecewise polynomial basis functions in space is employed. We discuss the structure of the system matrix and its efficient parallel assembly. ...

Although Gaussian elimination uses O(n) operations to invert an arbitrary matrix, matrices with a special Vandermonde structure can be inverted in only O(n) operations by the fast Traub algorithm. The original version of Traub algorithm was numerically unstable although only a minor modification of it yields a high accuracy in practice. The Traub algorithm has been extended from Vandermonde mat...

This workshop, sponsored by AIM and NSF, was devoted to β-generalizations of the classical ensembles in random matrix theory. Recent advances have put stochastic methods on center stage, thus explaining the workshop title ‘Brownian motion and random matrices’. One recalls that a viewpoint on classical random matrix theory, generalizing Dyson’s three fold way, is that physically relevant ensembl...

We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(C) and show that they have no odd-dimensional homology. We provide an explicit geometr...