401 citations · 542 across the 32 of their papers we have counts for
43 papers
Instability of Gaussian elimination is exponentially rare (proof of partial result)
Lloyd N. Trefethen
Gaussian elimination with partial pivoting is the standard algorithm for solving a dense system of linear equations . The ``growth factor'' for this process…
Reflections on the Millennium Problems
Lloyd N. Trefethen
In this essay I reflect on the status of three of the Millennium Prize problems: the Riemann Hypothesis, P vs. NP, and the solvability of the Navier-Stokes equations.
and rational approximation
Michael S. Ackermann, Sean Reiter, Lloyd N. Trefethen
Using recently developed algorithms, we compute and compare best and rational approximations of analytic functions on the unit disk. Although there is some theory…
Applications of AAA rational approximation
Yuji Nakatsukasa, Lloyd N. Trefethen
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
Quadrature formulas from rational approximations
Andrew Horning, Lloyd N. Trefethen
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approxim…
Numerical conformal mapping
Lloyd N. Trefethen
Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain in the complex plane (assuming ) can b…