A picture of me.

Alex Townsend

Assistant Professor

Cornell University

townsend@cornell.edu

Malott 589

CV


Here are three images from my research:

Papers

  1. A. Townsend, M. Stillman, and S. Strogatz, Circulant networks of identical Kuramoto oscillators: Seeking the densest network that does not self-synchronize and the sparsest one that does, submitted.

  2. S. Olver, A. Townsend, and G. Vasil, A sparse spectral method on triangles, submitted, pdf

  3. Y. Nakatsukasa and A. Townsend, Error localization of best L1 polynomial approximants, submitted, pdf

  4. B. Beckermann and A. Townsend, Bounds on the singular values of matrices with displacement structure, to appear in SIAM Review, 2019.

  5. A. Horning and A. Townsend, FEAST for differential eigenvalue problems, submitted, pdf

  6. T. Shi and A. Townsend, On the numerical ranks of tensors, submitted, pdf

  7. K. N. Quinn, H. Wilber, A. Townsend, and J. P. Sethna, Chebyshev approximation and the global geometry of sloppy models, to appear in Physical Review Letters, pdf.

  8. M. A. Gilles and A. Townsend, Continuous analogues of Krylov methods for differential operators, to appear in SINUM, pdf.

  9. S. Olver, A. Townsend, and G. M. Vasil, Recurrence relations for orthogonal polynomials on a triangle, submitted, pdf.

  10. A. Townsend and H. Wilber, On the singular values of matrices with high displacement rank, Lin. Alg. Appl., 548 (2018), pp. 19-41. pdf

  11. D. Fortunato and A. Townsend, Fast Poisson solvers for spectral methods, submitted, pdf

  12. J. Słomka, A. Townsend, and J. Dunkel, Stokes' second problem and an Einstein-de Haas analogue effect in active fluids, Physical Review Fluids, 3 (2018) pdf

  13. M. Udell and A. Townsend, Why are big data matrices approximately low rank?, SIMODS, 1 (2019), pp. 144-160. pdf

  14. D. Ruiz-Antolin and A. Townsend, A nonuniform fast Fourier transform based on low rank approximation, SISC, 40 (2018), A529-A547. pdf

  15. B. Beckermann and A. Townsend, On the singular values of matrices with displacement structure, SIMAX, 38 (2017), pp. 1227-1248. pdf

  16. L. Demanet and A. Townsend, Stable extrapolation of analytic functions, Found. Comput. Math., (2016), pp. 1-35. pdf

  17. A. Townsend, M. Webb, and S. Olver, Fast polynomial transforms based on Toeplitz and Hankel matrices, Math. Comp., 87 (2018), pp. 1913-1934. pdf

  18. H. Wilber, A. Townsend, and G. B. Wright, Computing with functions in spherical and polar geometrices II. The disk, SISC, 39 (2017), C238-C262. pdf

  19. A. Townsend, Gaussian elimination corrects pivoting mistakes, submitted, pdf

  20. A. Townsend, H. Wilber, and G. B. Wright, Computing with functions in spherical and polar geometries I. The sphere, SISC, 38 (2016), C403-C425. pdf

  21. V. Noferini and A. Townsend, Numerical instability of resultant methods for multidimensional rootfinding, SINUM, 54 (2016), pp. 719-743. pdf

  22. N. Hale and A. Townsend, A fast FFT-based discrete Legendre transform, IMA Numer. Anal., 36 (2016), pp. 1670-1684. pdf

  23. A.Townsend, A fast analysis-based discrete Hankel transform using asymptotic expansions, SINUM, 53 (2015), pp. 1897-1917. pdf

  24. A. Townsend, The race for high order Gauss-Legendre quadrature, in SIAM News, March 2015. pdf

  25. A. Townsend, T. Trogdon, and S. Olver, Fast computation of Gauss quadrature nodes and weights on the whole real line, IMA Numer. Anal., 36 (2016), pp. 337-358. pdf.

  26. S. Olver and A. Townsend, A practical framework for infinite-dimensional linear algebra, in HPTCDL 2014, IEEE press, pp. 57-62. pdf

  27. A. Townsend and S. Olver, The automatic solution of partial differential equations using a global spectral method, J. Comput. Phys., 299, 2015, pp. 106-123. pdf

  28. N. Hale and A. Townsend, An algorithm for the convolution of Legendre series, SISC, 36 (2014), A1207-A1220. pdf

  29. A. Townsend and L. N. Trefethen, Continuous analogues of matrix factorizations, Proc. R. Soc. A., 471 (2015). pdf

  30. N. Hale and A. Townsend, A fast, simple, and stable Chebyshev--Legendre transform using an asymptotic formula, SISC, 36 (2014), pp. A148-A167. pdf

  31. S. Olver and A. Townsend, Fast inverse transform sampling in one and two dimensions, submitted. pdf

  32. Y. Nakatsukasa, V. Noferini, and A. Townsend, Computing the common zeros of two bivariate functions via Bezout resultants, Numerische Mathematik, 129 (2015), pp 181-209. pdf

  33. A. Townsend and L. N. Trefethen, An extension of Chebfun to two dimensions, SISC, 35 (2013), pp. C495-C518. pdf

  34. Y. Nakatsukasa, V. Noferini, and A. Townsend, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, SIMAX, 38 (2017), pp. 1-29. pdf

  35. A. Townsend and L. N. Trefethen, Gaussian elimination as an iterative algorithm, SIAM News, March 2013. pdf

  36. N. Hale and A. Townsend, Fast and accurate computation of Gauss--Legendre and Gauss--Jacobi quadrature nodes and weights, SISC, 35 (2013), pp. A652-A672. pdf

  37. S. Olver and A. Townsend, A fast and well-conditioned spectral method, SIAM Review, 55 (2013), pp. 462-489. pdf

  38. A. Townsend and H. Wendland, Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values, IMA J. Numer. Anal., 33 (2013), pp. 1095-1114. pdf