Lloyd N. Trefethen
University of Oxford
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Featured researches published by Lloyd N. Trefethen.
Siam Review | 2004
Jean-Paul Berrut; Lloyd N. Trefethen
Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.
Siam Review | 1997
Lloyd N. Trefethen
If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ||An|| or ||exp(tA)||. More may be learned by examining the sets in the complex plane known as the pseudospectra of A, defined by level curves of the norm of the resolvent, ||(zI - A)-1||. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles.
Siam Review | 1981
Lloyd N. Trefethen
The relevance of group velocity to the behavior of finite difference models of time-dependent partial differential equations is surveyed and illustrated. Applications involve the propagation of wave packets in one and two dimensions, numerical dispersion, the behavior of parasitic waves, and the stability analysis of initial boundary-value problems.
SIAM Journal on Matrix Analysis and Applications | 1992
Noël M. Nachtigal; Satish C. Reddy; Lloyd N. Trefethen
Three leading iterative methods for the solution of nonsymmetric systems of linear equations are CGN (the conjugate gradient iteration applied to the normal equations), GMRES (residual minimization in a Krylov space), and CGS (a biorthogonalization algorithm adapted from the biconjugate gradient iteration). Do these methods differ fundamentally in capabilities? If so, which is best under which circumstances? The existing literature, in relying mainly on empirical studies, has failed to confront these questions systematically. In this paper it is shown that the convergence of CGN is governed by singular values and that of GMRES and CGS by eigenvalues or pseudo-eigenvalues. The three methods are found to be fundamentally different, and to substantiate this conclusion, examples of matrices are presented for which each iteration outperforms the others by a factor of size
Siam Journal on Scientific and Statistical Computing | 1979
Lloyd N. Trefethen
O(\sqrt N )
Acta Numerica | 1999
Lloyd N. Trefethen
or
Mathematics of Computation | 1986
Lloyd N. Trefethen; Laurence Halpern
O(N)
Mathematics of Computation | 2007
J. A. C. Weideman; Lloyd N. Trefethen
where N is the matrix dimension. Finally, it is shown that the performance of iterative methods for a particular mat...
SIAM Journal on Matrix Analysis and Applications | 1990
Lloyd N. Trefethen; Robert S. Schreiber
A program is described which computes Schwarz–Christoffel transformations that map the unit disk conformally onto the interior of a bounded or unbounded polygon in the complex plane. The inverse map is also computed. The computational problem is approached by setting up a nonlinear system of equations whose unknowns are essentially the “accessory parameters”
Numerische Mathematik | 1992
Satish C. Reddy; Lloyd N. Trefethen
z_k