Numerical analysis, scientific computing, and numerical algebraic geometry
I am interested in the study and development of numerical algorithms in applied mathematics. I mainly work in the following three areas: (1) Novel spectral methods for the solution of differential equations, (2) The asymptotics of special functions for image reconstruction, convolution, and quadrature, and (3) Numerical algebraic geometry for the solution of polynomial systems.
- Numerical instability of resultant method for multidimensional rootfinding (with V. Noferini), SIAM J. Numer. Anal., 54 (2016), 719-743.
- A fast analysis-based discrete Hankel transform using asymptotic expansions, SIAM J. Numer. Anal., 53 (2015), 1897-1917.
- An extension of Chebfun to two dimensions (with L. N. Trefethen), SIAM J. Sci. Comput., 35 (2013), C495-C518.
- Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights (with N. Hale), SIAM J. Sci. Comput., 35 (2013), A652-A672.
- A fast and well-conditioned spectral method (with S. Olver), SIAM Review, 55 (2013), 462-489.