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# Alex Townsend

Goenka Family Assistant Professor

### Departments/Programs

- Mathematics

### Graduate Fields

- Mathematics

## Research

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.

## Courses

### Fall 2020

- MATH 2940 : Linear Algebra for Engineers
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 7290 : Seminar on Scientific Computing and Numerics
- MATH 7510 : Berstein Seminar in Topology
- MATH 7610 : Topics in Geometry
- MATH 7670 : Topics in Algebraic Geometry
- MATH 7710 : Topics in Probability Theory
- MATH 7740 : Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning
- MATH 7810 : Seminar in Logic
- MATH 7900 : Supervised Reading and Research

## Publications

- 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.