Below you can find the research topics that I have worked on in the past or I am working right now. Generally speaking, I am interested in parallel numerical algorithms for the solution of large-scale linear systems, eigenvalue problems, and problems in data analysis.
Information on the authors as well as .pdf copies of the papers listed below can be found on my "Publications" webpage.
Numerical methods for the solution of linear systems
- 2. "A Hierarchical Low-Rank Schur Complement Preconditioner for Indefinite Linear Systems".
Preprint, Dept. Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 2017. - 1. "Accelerating Data Uncertainty Quantification By Solving Linear Systems with Multiple Right-Hand Sides".
Numerical Algorithms, Vol. 62, No. 4, pp. 637-653.
Numerical methods for the solution of the symmetric eigenvalue problem
- 3. "Beyond AMLS: Domain Decomposition with Rational Filtering".
Preprint, Dept. Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 2017. - 2. "Domain Decomposition Approaches for Accelerating Contour Integration Eigenvalue Solvers for Symmetric Eigenvalue Problems."
To appear in Numerical Linear Algebra with Applications, 2018. - 1. "Spectral Schur Complement Techniques for Symmetric Eigenvalue Problems".
Electronic Transactions on Numerical Analysis, Vol. 45, pp. 305-329, 2016.
Matrix functions in general
- 2. "Stable Computation of Generalized Matrix Functions via Polynomial Interpolation".
Preprint, Dept. Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 2017. - 1. "Estimating the Trace of the Matrix Inverse by Interpolating from the Diagonal of an Approximate Inverse".
Journal of Computational Physics, Vol. 326, pp. 828-844, 2016.