Eric Hallman

Contact

Email: erhallma at ncsu dot edu
Office: SAS 3110

Research

My research interests lie in numerical linear algebra, particularly in error estimation for iterative methods, randomized roundoff error analysis, matrix sketching, and stochastic trace estimation.

CV

Publications and Preprints

H. Al Daas, G. Ballard, P. Cazeaux, E. Hallman, A. Miedlar, M. Pasha, T.W. Reid, A.K. Saibaba, Randomized algorithms for rounding in the Tensor-Train format, 2021. pdf arXiv

E. Hallman and I. Ipsen, Deterministic and probabilistic error bounds for floating point summation algorithms, 2021. pdf arXiv

E. Hallman, A refined probabilistic error bound for sums, 2021. pdf arXiv

E. Hallman and D. Troester, A multilevel approach to stochastic trace estimation, in revision, 2021. pdf arXiv

E. Hallman, A block bidiagonalization method for fixed-accuracy low-rank matrix approximation, in revision, 2021. pdf arXiv

E. Hallman, Faster stochastic trace estimation with a Chebyshev product identity, Applied Mathematics Letters 120, 107246, 2021. pdf online

E. Hallman, Estimating the backward error for the least-squares problem with multiple right-hand sides, Linear Algebra Appl. 605 (2020), pp. 227-238. pdf online

E. Hallman, Sharp 2-norm error bounds for LSQR and the conjugate gradient method, Siam J. Matrix Anal. Appl. 41(3) (2020), pp. 1183-1207. pdf online

E. Hallman and M. Gu, LSMB: minimizing the backward error for least-squares problems, Siam J. Matrix Anal. Appl. 39(3) (2018), pp. 1295--1317. pdf online

Talks

• A block bidiagonalization method for fixed-precision low-rank matrix approximation, SIAM Conference on Applied Linear Algebra (May 2021). Talk delivered remotely.
• Sharp 2-norm error bounds for the conjugate gradient method and LSQR, SAMSI Postdoctoral Fellow Seminar (Sepember 2020). Talk delivered remotely.
• Sharp 2-norm error bounds for the conjugate gradient method and LSQR, Householder Symposium XXI (June 2020, postponed to June 2022).
• Sharp 2-norm error bounds for LSQR and the conjugate gradient method, NA Seminar, North Carolina State University (October 2019).
• Adapting Craig's method for least-squares problems, Linear Algebra and Optimization Seminar, Stanford University (November 2018).
• LSMB: minimizing the backward error in iterative methods for least-squares problems, Linear Algebra and Optimization Seminar, Stanford University (October 2016).

Code

• Github repo
• LSMB: an iterative solver for least-squares problems.
• 2-norm error estimates for least-squares and SPD problems.

Teaching

• Fall 2021: Math 402, Mathematics of Scientific Computing
• Spring 2021: Math 402, Mathematics of Scientific Computing
• Fall 2020: Math 402, Mathematics of Scientific Computing
• Spring 2019: Math 402, Mathematics of Scientific Computing
• Fall 2019: Math 114, Finite Mathematics

• Spring 2019: Math 98, Introduction to MATLAB
• Fall 2018: Math 98, Introduction to MATLAB
• Summer 2018: Math 55, Discrete Mathematics
• Spring 2018: Math 98, Introduction to MATLAB
• Summer 2015: Math 55, Discrete Mathematics