8th Croatian Mathematical Congress

Session

Numerical Analysis and Scientific Computing

NA

2 Jul 2024, 17:30

D9 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Conveners

Numerical Analysis and Scientific Computing

• Ivan Slapničar (University of Split, FESB)

Numerical Analysis and Scientific Computing

• Zlatko Drmac (faculty of Science, Department of Mathematics, University of Zagreb)

119. Convergence of the complex block Jacobi methods

Erna Begovic Kovac (University of Zagreb)

02/07/2024, 17:30

NA: Numerical Analysis and Scientific Computing

Talk

The Jacobi method is a well known iterative method for solving the symmetric eigenvalue problem. Efficiency of the Jacobi method can be improved if the algorithm works on the matrix blocks instead of the elements.

In this talk we consider the convergence of the complex block Jacobi diagonalization methods under the large set of the generalized serial pivot strategies. We present the...

149. Computing Eigenvalue Decomposition of Arrowhead and Diagonal-Plus-Rank-$k$ Matrices of Quaternions

Prof. Ivan Slapničar (University of Split, FESB)

02/07/2024, 17:50

NA: Numerical Analysis and Scientific Computing

Talk

We present algorithms for solving the eigenvalue problem for the arrowhead and diagonal-plus-rank-$k$ matrices of quaternions. The algorithms use the Rayleigh Quotient Iteration with double shift combined with Wielandt's deflation technique. Since each eigenvector can be computed in $O(n)$ operations, the algorithms require $O(n^2)$ floating-point operations, $n$ being the order of the matrix....

147. Koopman-Schur decomposition for data driven analysis

Zlatko Drmac (faculty of Science, Department of Mathematics, University of Zagreb)

03/07/2024, 11:05

NA: Numerical Analysis and Scientific Computing

Talk

The Dynamic Mode Decomposition (DMD) is a tool of the trade in computational data driven analysis of complex dynamical systems, e.g. fluid flows, where it can be used to reveal coherent structures by decomposing the flow field into component fluid structures, called DMD modes, that describe the evolution of the flow. The theoretical underpinning of the DMD is the Koopman composition operator...

154. Solving Bilevel Optimization Problems Using Deep Learning

Domagoj Vlah (University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Mathematics)

03/07/2024, 11:25

NA: Numerical Analysis and Scientific Computing

Talk

We propose an effective numerical scheme involving deep learning to approximate solution to bilevel optimization problems of size that is considered computationally intractable using known approaches. The lower level is bypassed completely by training a deep neural network to approximate the relevant lower-level effect on the upper level. We illustrate this method on solving bilevel power...

159. Marker gene methods for cell discrimination in single-cell RNA-seq data

Bartol Borozan (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek), Luka Borozan (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

03/07/2024, 11:45

NA: Numerical Analysis and Scientific Computing

Talk

Single-cell RNA-seq (scRNA-seq) produces a plethora of data from which one can derive information about gene expression levels for individual cells. In order to efficiently classify cells based on the tissues they originated from, it is crucial to identify and select informative genes is preserve the differences occurring between distinct cell types while excluding as much redundant...