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. V. Kalantzis, C. Bekas, A. Curioni, and E. Gallopoulos, "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.
  • 2. V. Kalantzis, J. Kestyn, E. Polizzi, and Y. Saad, "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. V. Kalantzis, R. Li, and Y. Saad, "Spectral Schur Complement Techniques for Symmetric Eigenvalue Problems". Electronic Transactions on Numerical Analysis, Vol. 45, pp. 305-329, 2016.

  • Trace of 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. L. Wu, J. Laeuchli, V. Kalantzis, A. Stathopoulos, and E. Gallopoulos "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.