Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Balabanov, Oleg"'
Autor:
Melnichenko, Maksim, Balabanov, Oleg, Murray, Riley, Demmel, James, Mahoney, Michael W., Luszczek, Piotr
This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with large row counts. The algorithm combines methods from randomized numerical linear algebra in a particularly careful way in
Externí odkaz:
http://arxiv.org/abs/2311.08316
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce quasi-optimal approxim
Externí odkaz:
http://arxiv.org/abs/2302.07466
Publikováno v:
Proceedings of the International Conference on Machine Learning, pp. 1564-1576. PMLR, 2023
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian matrices, on
Externí odkaz:
http://arxiv.org/abs/2210.11295
Autor:
Balabanov, Oleg
This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently computable random
Externí odkaz:
http://arxiv.org/abs/2210.09953
Autor:
Balabanov, Oleg, Grigori, Laura
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having at least as
Externí odkaz:
http://arxiv.org/abs/2111.14641
Autor:
Balabanov, Oleg, Nouy, Anthony
The performance of projection-based model order reduction methods for solving parameter-dependent systems of equations highly depends on the properties of the operator, which can be improved by preconditioning. In this paper we present strategies to
Externí odkaz:
http://arxiv.org/abs/2104.12177
Autor:
Balabanov, Oleg, Grigori, Laura
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least as numeri
Externí odkaz:
http://arxiv.org/abs/2011.05090
Autor:
Balabanov, Oleg, Nouy, Anthony
Publikováno v:
Adv Comput Math 47, 26 (2021)
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct a reduced
Externí odkaz:
http://arxiv.org/abs/1910.14378
Autor:
Balabanov, Oleg, Nouy, Anthony
Publikováno v:
Adv Comput Math 45, 2969-3019 (2019)
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of low-dimens
Externí odkaz:
http://arxiv.org/abs/1803.02602
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