200 Union St. SE
5-250 Keller Hall
Minneapolis, MN 55414
Tel: +1 (612) 636-2896
Email: kalan019@umn.edu

Photo of Minneapolis.

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. 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.
  1. 3. "Beyond AMLS: Domain Decomposition with Rational Filtering".
    Preprint, Dept. Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 2017.
  2. 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.
  3. 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. 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.