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.
Numerical methods for the solution of linear systems
Mean relative error of a Monte Carlo stochastic estimator to approximate the diagonal of the inverse of a model covariance matrix.
- 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
The Newton Branch-hopping scheme to compute the
two smallest eigenvalues of a 2D discretized Laplacian.
- 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."
Preprint, Dept. Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 2016. - 1. "Spectral Schur Complement Techniques for Symmetric Eigenvalue Problems".
Electronic Transactions on Numerical Analysis, Vol. 45, pp. 305-329, 2016.
Matrix functions
An example of fitting the approximate diagonal of the matrix inverse using PCHIP. Red: the true diagonal entries. Blue: the original approximation. Green: The fitted approximation.
- 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.