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)
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...
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....
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...
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...
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...
