Decompositions and Approximations of Matrices and Tensors
DAMAT


Installation Research Project funded by Croatian science foundation
Code: 2019-04-5200
Duration: January 2020 - December 2024 (60 months)
Total value: 1.007.800,00 HRK

Contact: ebegovic [at] fkit.hr

About


The most important and the most challenging problems of the scientific computing are those involving very big amount of numerical data modelled by big matrices or multidimensional tensors. Limitations of the computer memory and the fact that we want to obtain the solution fast imply additional requirements to our problems. We can overcome these obstacles by well-created algorithms that efficiently use computer memory while keeping the relative accuracy. Some of the approaches in this direction are using the particular structure of the problem in question, using low-rank approximations of matrices or tensors, and using matrix or tensor decompositions. Our group works on hot topics of numerical linear algebra where many interesting questions are raised, both theoretical ones and those involving various applications.

Proposed research can be split into the following six sections: (1) Numerical algorithms for tensors, (2) Structure-preserving matrix and tensor approximations, (3) Algorithms for the nonlinear eigenvalue problem, (4) Applications of matrix decompositions in ultrasound tomography, (5) Jacobi-type methods for the eigenvalue problem, and (6) Coupled decompositions.

Keywords: numerical linear algebra, scientific computing, factorization, aproximation, eigendecomposition, structure-preserving algorithms

Principal investigator

  • Erna Begović Kovač, assistant professor, Faculty of Chemical Engineering and Technology, University of Zagreb

Team members

  • Ana Bokšić, PhD student, Faculty of Chemical Engineering and Technology, University of Zagreb
  • Anita Carević, postdoc, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split
  • Lana Periša, R&D engineer, Visage Technologies d.o.o.
  • Ivana Šain Glibić, postdoc, Department of Mathematics, Faculty of Science, University of Zagreb

Research publications

  1. Z. Drmač, I. Šain Glibić: An algorithm for the complete solution of the quartic eigenvalue problem
    submitted for publication [arXiv]
  2. R. Van Beeumen, L. Periša, D. Kressner, C. Yang: A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems
    submitted for publication [arXiv]
  3. E. Begović Kovač: Finding the closest normal structured matrix
    Linear Algebra Appl. 617 (2021) 49-77. [journal] [arXiv]
  4. E. Begović Kovač: Hybrid CUR-type decomposition of tensors in the Tucker format
    submitted for publication [arXiv]

Dissemination

  • September 2020, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
    E. Begović Kovač: Hybrid CUR-type decomposition of tensors in the Tucker format (talk)
  • September 2020, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
    A. Carević: Determination of the regularization parameter for the distorted Born iterative method (talk)
  • September 2020, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
    I. Šain Glibić: New numerical algorithm for deflation of infinite and zero eigenvalues and full solution of quadratic eigenvalue problems (talk)
  • February 2020, Georgia Scientific Computing Symposium, Emory University, Atlanta GA, USA
    E. Begović Kovač: On the convergence of complex Jacobi methods (poster)

News

  • Ana Bokšić joined the project in October 2020.
  • Project presentation will take place online via Zoom on June 8th 2020, starting at 4 pm.
  • We are looking for a PhD student to start from October 2020. For more information contact Erna Begović Kovač, ebegovic [at] fkit.hr.