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Alex Townsend
Goenka Family Assistant Professor
Departments/Programs
 Mathematics
Graduate Fields
 Mathematics
Research
Numerical analysis, scientific computing, and deep learning
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) Lowrank techniques, and (3) Theoretical aspects of deep learning.
Courses
Fall 2021
 MATH 2210 : Linear Algebra
 MATH 4900 : Supervised Research
 MATH 4901 : Supervised Reading
 MATH 7290 : Seminar on Scientific Computing and Numerics
Publications

Dense networks that do not synchronize and sparse ones that do (with M. Stillman and S. H. Strogatz), Chaos, 30 (2020), 083142.

Fast algorithms using orthogonal polynomials (with S. Olver and R. M. Slevinsky), Acta Numerica, 29 (2020), pp. 573699.

Stable extrapolation of analytic functions (with L. Demanet), Foundations of Computational Mathematics, 19 (2019), pp. 297331.

Bounds on the singular values of matrices with displacement structure (with B. Beckermann), SIAM Review, 61 (2019), pp. 319344.

Why are big data matrices approximately low rank? (with M. Udell), SIAM Journal on Mathematics of Data Science, 1 (2019), pp. 144160.