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pro vyhledávání: '"Novaković, Vedran"'
Autor:
Novaković, Vedran
An enhanced Kogbetliantz method for the singular value decomposition (SVD) of general matrices of order two is proposed. The method consists of three phases: an almost exact prescaling, that can be beneficial to the LAPACK's xLASV2 routine for the SV
Externí odkaz:
http://arxiv.org/abs/2407.13116
Autor:
Novaković, Vedran
Publikováno v:
J. Comput. Appl. Math. 450 (2024) 116003
This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and $\mathtt{cr\_rsqrt}$, pr
Externí odkaz:
http://arxiv.org/abs/2308.14222
Autor:
Novaković, Vedran
Publikováno v:
SIAM J. Sci. Comput. 45 (2023), 3; C73-C100
The eigenvalue decomposition (EVD) of (a batch of) Hermitian matrices of order two has a role in many numerical algorithms, of which the one-sided Jacobi method for the singular value decomposition (SVD) is the prime example. In this paper the batche
Externí odkaz:
http://arxiv.org/abs/2202.08361
Autor:
Novaković, Vedran
Publikováno v:
Parallel Process. Lett. 30 (2020), 4; 2050015
In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch of matric
Externí odkaz:
http://arxiv.org/abs/2005.07403
Autor:
Novaković, Vedran, Singer, Sanja
Publikováno v:
Numer. Algoritms 90 (2022), 2; 523-561
In this paper a two-sided, parallel Kogbetliantz-type algorithm for the hyperbolic singular value decomposition (HSVD) of real and complex square matrices is developed, with a single assumption that the input matrix, of order $n$, admits such a decom
Externí odkaz:
http://arxiv.org/abs/2003.06701
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Autor:
Novaković, Vedran, Singer, Sanja
Publikováno v:
Int. J. High Perform. Comput. Appl. 35 (2021), 2; 170-205
A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both of the full
Externí odkaz:
http://arxiv.org/abs/1909.00101
Publikováno v:
SIAM J. Sci. Comput. 42 (2020), C265-C293
In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$
Externí odkaz:
http://arxiv.org/abs/1907.08560
Autor:
Novaković, Vedran
Publikováno v:
SIAM J. Sci. Comput. 37 (2015), C1-C30
We present a hierarchically blocked one-sided Jacobi algorithm for the singular value decomposition (SVD), targeting both single and multiple graphics processing units (GPUs). The blocking structure reflects the levels of GPU's memory hierarchy. The
Externí odkaz:
http://arxiv.org/abs/1401.2720
Autor:
Singer, Sanja, Singer, Sasa, Novakovic, Vedran, Davidovic, Davor, Bokulic, Kresimir, Uscumlic, Aleksandar
Publikováno v:
Appl. Math. Comput. 218 (2012) 5704-5725
The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancin
Externí odkaz:
http://arxiv.org/abs/1008.4166