Main Research Interests

My PhD research is in a subfield of numerical linear algebra (NLA) that deals with large-scale sparse symmetric eigenvalue and singular value computations. Such calculations are very important in many other fields such as data science, machine learning, and spectral graph theory.

The primary goal of this work is to improve algorithms that compute an approximation to a subset of desired eigenpairs or singular triplets of a very large matrix. A notable concentration has been on an intermediate step in these classical procedures: the deflation of eigenvalues or singular values from a small tridiagonal or bidiagonal matrix, using algorithms such as $QR$.

To support the mathematical development of my work, I have written a large amount of MATLAB software. Some publically available projects are on GitHub and can be accessed from my software page.

In addition to eigenvalue and singular value algorithms, I have some experience in iterative methods for nonsymmetric linear systems such as GMRES (in particular, augmentation and deflation strategies). In the future, I hope to dip more into randomized NLA algorithms that are in the spotlight right now.