Zobrazeno 1 - 10
of 226
pro vyhledávání: '"DRMAČ, ZLATKO"'
Autor:
Drmač, Zlatko, Mezić, Igor
This paper introduces a new theoretical and computational framework for a data driven Koopman mode analysis of nonlinear dynamics. To alleviate the potential problem of ill-conditioned eigenvectors in the existing implementations of the Dynamic Mode
Externí odkaz:
http://arxiv.org/abs/2312.15837
The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed step size
Externí odkaz:
http://arxiv.org/abs/2311.02031
Autor:
Mezic, Igor, Drmac, Zlatko, Crnjaric-Zic, Nelida, Macesic, Senka, Fonoberova, Maria, Mohr, Ryan, Avila, Allan, Manojlovic, Iva, Andrejcuk, Aleksandr
The problem of prediction of behavior of dynamical systems has undergone a paradigm shift in the second half of the 20th century with the discovery of the possibility of chaotic dynamics in simple, physical, dynamical systems for which the laws of ev
Externí odkaz:
http://arxiv.org/abs/2304.13601
Publikováno v:
SIAM Journal on Mathematics of Data Science, 5, 97-121, 2023
Invariant Coordinate Selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an independe
Externí odkaz:
http://arxiv.org/abs/2207.02131
Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues. In the original formulation of HSV
Externí odkaz:
http://arxiv.org/abs/2012.11734
Autor:
Manojlović, Iva, Fonoberova, Maria, Mohr, Ryan, Andrejčuk, Aleksandr, Drmač, Zlatko, Kevrekidis, Yannis, Mezić, Igor
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced map, we ca
Externí odkaz:
http://arxiv.org/abs/2006.11765
Autor:
Drmač, Zlatko
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that guarantee
Externí odkaz:
http://arxiv.org/abs/2006.02753
Autor:
Bujanović, Zvonimir, Drmač, Zlatko
In this note we describe two modifications of the ScaLAPACK subroutines PxGEQPF for computing the QR factorization with the Businger-Golub column pivoting. First, we resolve a subtle numerical instability in the same way as we have done it for the LA
Externí odkaz:
http://arxiv.org/abs/1910.05623
Autor:
Drmač, Zlatko, Peherstorfer, Benjamin
Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements. This work investigates the robustness of the Loewner approach to noise. The key finding is that if the mea
Externí odkaz:
http://arxiv.org/abs/1910.00110