Welcome!

I am an NSF postdoctoral fellow with the Oden Institute at University of Texas at Austin. I work with Gunnar Martinsson's research group in numerical analysis and computational mathematics. I graduated from Cornell's applied mathematics program, where my PhD work was supervised by Prof. Alex Townsend. Broadly speaking, my research considers the intersection of approximation theory, numerical linear algebra, and scientific computing. My projects involve the development and analysis of direct methods for solving PDEs, low rank and rank-structured approximation methods, numerical methods for solving Sylvester and Lyapunov matrix equations, numerical methods for computing with polynomial approximations to functions, and robust numerical methods for constructing and computing with rational approximations to functions.

CV (pdf)

Research

Papers

  • H. Wilber, A. Damle, and A. Townsend, Data-driven algorithms for signal processing with trigonometric rational functions, SISC, 44-3 (2022), C185-C209 (pdf)
  • D. Rubin, A. Townsend,and H. Wilber, Bounding Zolotarev numbers using Faber rational functions, Const. Approx., 56 (2022), 1-26 (pdf)
  • Quinn, K., Wilber, H., Townsend, A., Sethna, J.P., Chebyshev approximation and the global geometry of model predictions, Phy. Rev. Let. (2019), 122(15), 158302. (pdf)
  • A. Townsend and H. Wilber, On the singular values of matrices with high displacement rank, LAA, 548 (2018), 19-41. (pdf)
  • H. Wilber, A. Townsend, and G. B. Wright, Computing with functions in spherical and polar geometries II. The disk, SISC, 39 (2017), C238-C262. (pdf)
  • 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)

Theses

Upcoming Conferences, Visits, Talks

Selected Presentations

    (click here for complete list.)
  • Rational approximation and what we can learn from the square root.(slides)
  • REfit:Data-driven computing with trigonometric rationals. (poster)
  • Low rank numerical methods via rational approximation. (slides)
  • Designing low rank methods for matrices with displacement structure. (slides)
  • Computing with rational approximations in signal processing. (slides)
  • Compression properties in rank-structured Toeplitz solvers. (slides)
  • The singular values of matrices with high displacement rank. (slides)
  • Numerical computing with functions in polar and spherical geometries. (slides)
  • Computing with functions on the sphere and disk. (poster)

Software

  • REfit (computing with rational functions and exponential sums)
  • FI-ADI (low rank solver for Sylvester matrix equations)
  • Diskfun (computing with functions on the unit disk)
  • Spherefun (computing with functions on the unit sphere)

Awards and Fellowships

    (click here for complete list.)
  • Householder Prize (2022)
  • AWM 2022 Dissertation Prize
  • NSF Mathematical Sciences Postdoctoral Research Fellowship (2021-2023)
  • SIAM UKIE prize: Best student presentation, 27th Biennial Numerical Analysis Conference (2019)
  • NSF Graduate Research Fellowship (2016-2020)
  • M.S. thesis selected as the Boise State Univ. 2017 Distinguished Thesis in STEM
  • NASA ISGC fellowship (2015-2016)

Teaching

  • Spring 2023: (Instructor) M408D, Sequences, Series and Multivariable Calculus. Click here for a copy of the course syllabus
  • Fall 2022: (Instructor) M427L, Advanced calculus for applications, II. Click here for a copy of the course syllabus
  • Spring 2021: (TA with instructor Prof. Steven Strogatz) M1300: Mathematical explorations
  • Fall 2020: (TA with instructor Prof. Alex Townsend) M2940: Linear algebra for engineers

Contact

Office:POB 3.420

Email: heather (dot) wilber@oden (dot) utexas (dot) edu

Address:
Oden Institute for Computational Engineering and Sciences
Univerity of Texas at Austin
201 E. 24th Street
Austin, Texas 78712