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
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Dissemination
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September 2024, Applied Mathematics and Scientific Computing (ApplMath), Dubrovnik, Croatia
E. Begović Kovač: Randomized algorithms for coupled decompositions (talk)
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September 2024, Applied Mathematics and Scientific Computing (ApplMath), Dubrovnik, Croatia
A. Perković: Convergence of the Eberlein diagonalization method under generalized serial pivot strategies (talk)
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July 2024, 8th Croatian Mathematical Congress, Osijek, Croatia
E. Begović Kovač: Convergence of the complex block Jacobi methods (talk)
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May 2024, SIAM Conference on Applied Linear Algebra, Paris, France
E. Begović Kovač: Jacobi-Type Methods for Tensor Decompositions (talk)
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May 2024, SIAM Conference on Applied Linear Algebra, Paris, France
A. Carević: Double Randomized Generalized SVD Regularization Algorithm (poster)
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January 2024, European Women in Mathemathematics Hrvatska
E. Begović Kovač: Dekompozicije i aproksimacije tenzora (talk)
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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)
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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)
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August 2023, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokyo, Japan
E. Begović Kovač: Convergence of the Eberlein diagonalization method (talk)
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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)
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May 2023, UNIC Mathematics Workshop, Zagreb, Croatia
E. Begović Kovač: Tensor diagonalization algorithms (talk)
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April 2023, 7th Faculty of Science PhD Student Symposium, Zagreb, Croatia
A. Perković: Trace maximization algorithm for the
approximate tensor diagonalization (talk)
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March 2023, Seminar za numeričku matematiku i znanstveno računanje, Zagreb, Croatia
A. Perković: Algoritmi i konvergencija metoda Jacobijevog tipa (obrana teme doktorske disertacije)
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October 2022, IEEE International Ultrasonics Symposium (IUS), Venice, Italy
A. Carević: Automating regularization parameter selection of the inverse problem in ultrasound tomography (poster)
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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
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September 2022, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
A. Perković: Trace maximization algorithm for the approximate tensor diagonalization (poster)
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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
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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)
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October 2021, Mat Triad, Tomar, Portugal (online)
I. Šain Glibić: An algorithm for the complete solution of quartic eigenvalue problem (talk)
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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)
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July 2021, Applied Mathematics Workshop, Brijuni, Croatia
E. Begović Kovač: Jacobi-type method for the SVD-like tensor decomposition (talk)
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July 2021, Seminar za numeričku matematiku i znanstveno računanje, Zagreb, Croatia
E. Begović Kovač: Hibridna CUR dekompozicija tenzora (talk)
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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)
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June 2021, 8th European Congress of Mathematics, Portorož, Slovenia (online)
L. Periša: Infinite Tensor Rings (talk)
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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)
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September 2020, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
E. Begović Kovač: Hybrid CUR-type decomposition of tensors in the Tucker format (talk)
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September 2020, Applied Mathematics and Scientific Computing (ApplMath), Brijuni, Croatia
A. Carević: Determination of the regularization parameter for the distorted Born iterative method (talk)
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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)
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February 2020, Georgia Scientific Computing Symposium, Emory University, Atlanta GA, USA
E. Begović Kovač: On the convergence of complex Jacobi methods (poster)
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