10 research outputs found
A weakly stable algorithm for general Toeplitz systems
We show that a fast algorithm for the QR factorization of a Toeplitz or
Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A.
Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx =
A^Tb, we obtain a weakly stable method for the solution of a nonsingular
Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the
solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further
details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm
Theory of charged impurity scattering in two dimensional graphene
We review the physics of charged impurities in the vicinity of graphene. The
long-range nature of Coulomb impurities affects both the nature of the ground
state density profile as well as graphene's transport properties. We discuss
the screening of a single Coulomb impurity and the ensemble averaged density
profile of graphene in the presence of many randomly distributed impurities.
Finally, we discuss graphene's transport properties due to scattering off
charged impurities both at low and high carrier density.Comment: Invited review for the graphene special issue of Solid State
Communications. Related papers available at http://www.physics.umd.edu/cmtc