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, associate professor, Faculty of Chemical Engineering and Technology, University of Zagreb

Team members

  • Ana Perković (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, Visage Technologies, Zagreb
  • Ivana Šain Glibić, assistant professor, Department of Mathematics, Faculty of Science, University of Zagreb

Research publications

  1. E. Begović Kovač, A. Carević, I. Šain Glibić: Randomized coupled decompositions
    Submitted for publication. [arXiv]
  2. E. Begović Kovač, V. Hari: Convergence of the complex block Jacobi methods under the generalized serial pivot strategies
    Linear Algebra Appl. 699 (2024) 421-458. [journal] [arXiv]
  3. E. Begović Kovač, L. Periša: CP decomposition and low-rank approximation of antisymmetric tensors
    Electron. Trans. Numer. Anal. 62 (2024) 72-94. [journal] [arXiv]
  4. E. Begović Kovač, A. Perković: Convergence of the Eberlein diagonalization method under the generalized serial pivot strategies
    Electron. Trans. Numer. Anal. 60 (2024) 238-255. [journal] [arXiv]
  5. A. Carević, I. Slapničar, M. Almekkawy: Automating regularization parameter selection of the inverse problem in ultrasound tomography
    In 2022 IEEE International Ultrasonics Symposium (IUS) (2022) 1-4. [journal]
  6. E. Begović Kovač, A. Perković: Trace maximization algorithm for the approximate tensor diagonalization
    Linear Multilinear Algebra 72(3) (2024) 429-450. [journal] [arXiv]
  7. E. Begović Kovač: Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization
    Calcolo 60, 3 (2023). [journal] [arXiv]
  8. A. Carević, I. Slapničar, M. Almekkawy: Solving Ultrasound Tomography’s Inverse Problem: Automating Regularization Parameter Selection
    IEEE Trans Ultrason Ferroelectr Freq Control 69(8) (2022) 2447-2461. [journal]
  9. Z. Drmač, I. Šain Glibić: An algorithm for the complete solution of the quartic eigenvalue problem
    ACM Transactions on Mathematical Software (TOMS) 48(1) (2022) 4, 1-34. [journal] [arXiv]
  10. R. Van Beeumen, L. Periša, D. Kressner, C. Yang: A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems
    Numer Linear Algebra Appl. (2024) e2573. [journal] [arXiv]
  11. E. Begović Kovač: Finding the closest normal structured matrix
    Linear Algebra Appl. 617 (2021) 49-77. [journal] [arXiv]
  12. E. Begović Kovač: Hybrid CUR-type decomposition of tensors in the Tucker format
    BIT Numer. Math. 62(1) (2022) 125-138. [journal] [arXiv]

Dissemination

  • September 2024, Applied Mathematics and Scientific Computing (ApplMath), Dubrovnik, Croatia
    E. Begović Kovač: Randomized algorithms for coupled decompositions (talk)
  • September 2024, Applied Mathematics and Scientific Computing (ApplMath), Dubrovnik, Croatia
    A. Perković: Convergence of the Eberlein diagonalization method under generalized serial pivot strategies (talk)
  • July 2024, 8th Croatian Mathematical Congress, Osijek, Croatia
    E. Begović Kovač: Convergence of the complex block Jacobi methods (talk)
  • May 2024, SIAM Conference on Applied Linear Algebra, Paris, France
    E. Begović Kovač: Jacobi-Type Methods for Tensor Decompositions (talk)
  • May 2024, SIAM Conference on Applied Linear Algebra, Paris, France
    A. Carević: Double Randomized Generalized SVD Regularization Algorithm (poster)
  • January 2024, European Women in Mathemathematics Hrvatska
    E. Begović Kovač: Dekompozicije i aproksimacije tenzora (talk)
  • September 2023, 21st IMACS (International Association for Mathematics and Computers in Simulation) World Congress, Rome, Italy
    A. Carević: Randomized GSVD based regularization for the inverse problem of ultrasound tomography (poster)
  • September 2023, 10th Workshop on Matrix Equations and Tensor Techniques (METT), Aachen, Germany
    E. Begović Kovač: CP decomposition and low-rank approximation of antisymmetric tensors (talk)
  • August 2023, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokyo, Japan
    E. Begović Kovač: Convergence of the Eberlein diagonalization method (talk)
  • June 2023, 25th Conference of the International Linear Algebra Society (ILAS), Madrid, Spain
    E. Begović Kovač: CP decomposition and low-rank approximation of antisymmetric tensors (talk)
  • May 2023, UNIC Mathematics Workshop, Zagreb, Croatia
    E. Begović Kovač: Tensor diagonalization algorithms (talk)
  • April 2023, 7th Faculty of Science PhD Student Symposium, Zagreb, Croatia
    A. Perković: Trace maximization algorithm for the approximate tensor diagonalization (talk)
  • March 2023, Seminar za numeričku matematiku i znanstveno računanje, Zagreb, Croatia
    A. Perković: Algoritmi i konvergencija metoda Jacobijevog tipa (obrana teme doktorske disertacije)
  • October 2022, IEEE International Ultrasonics Symposium (IUS), Venice, Italy
    A. Carević: Automating regularization parameter selection of the inverse problem in ultrasound tomography (poster)
  • September 2022, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
    A. Carević: Analyzing different versions of randomized (G)SVD for regularization of large scale discrete inverse problems (poster) - Honorable mention in the category Best poster presentations
  • September 2022, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
    A. Perković: Trace maximization algorithm for the approximate tensor diagonalization (poster)
  • July 2022, Short Communications Satellite 2022 of the International Congress of Mathematicians (online)
    E. Begović Kovač: Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization (slides) - 3rd place in the category Most voted
  • June 2022, 24th Conference of the International Linear Algebra Society (ILAS), Galway, Ireland
    I. Šain Glibić: Importance of the deflation process for the solution of quartic eigenvalue problem (talk)
  • October 2021, Mat Triad, Tomar, Portugal (online)
    I. Šain Glibić: An algorithm for the complete solution of quartic eigenvalue problem (talk)
  • September 2021, GAMM Workshop Applied and Numerical Linear Algebra, Potsdam, Germany
    E. Begović Kovač: Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization (talk)
  • July 2021, Applied Mathematics Workshop, Brijuni, Croatia
    E. Begović Kovač: Jacobi-type method for the SVD-like tensor decomposition (talk)
  • July 2021, Seminar za numeričku matematiku i znanstveno računanje, Zagreb, Croatia
    E. Begović Kovač: Hibridna CUR dekompozicija tenzora (talk)
  • June 2021, 8th European Congress of Mathematics, Portorož, Slovenia (online)
    E. Begović Kovač: On the convergence of the Jacobi-type method for computing orthogonal tensor decomposition (talk)
  • June 2021, 8th European Congress of Mathematics, Portorož, Slovenia (online)
    L. Periša: Infinite Tensor Rings (talk)
  • May 2021, SIAM Conference on Applied Linear Algebra, New Orleans LA, USA (online)
    E. Begović Kovač: Finding the Closest Normal Structured Matrix (talk)
  • May 2021, Scientific Colloquium of the Croatian Mathematical Society, Zagreb, Croatia
    E. Begović Kovač: Convergence of the block Jacobi methods (invited talk)
  • 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)