Computation on GPU of Eigenvalues and Eigenvectors of a Large Number of Small Hermitian Matrices

Cosnuau, A.

doi:10.1016/j.procs.2014.05.072

Cited by 19 publications

(13 citation statements)

References 2 publications

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“…In [16] this issue has been discussed further, with a conclusion that the Diakonov determinant can remain positive definite at higher densities needed, but only provided certain correlations in the dyon locations are enforced. We have therefore used the Householder QR algorithm together with tri-diagolization of the matrix G [19] to find the eigenvalues. We also redefine the potential as follows:…”

Section: The Instanton-dyon Interactionsmentioning

confidence: 99%

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Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Larsen

Shuryak

2015

Phys. Rev. D

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Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory, using standard Metropolis Monte Carlo and integration over parameter methods. We calculate the free energy as a function of the holonomy (logarithm of the Polyakov line) , the dyon densities, and the Debye mass, and find its minima as a function of those parameters. Unlike previous numerical study of such ensemble, we show that the back reaction on the holonomy potential does generate confinement, provided the density is sufficiently high (or the temperature sufficiently low). We then report various properties of the self-consistent ensembles as a function of temperature.

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Section: The Instanton-dyon Interactionsmentioning

confidence: 99%

“…While the practical cost of the simulations restricts the number of points one can study, we still had generated more than hundred thousand runs and multiple 7 6 which deions, and iables. (19) explicitly with the er is the p g in the onov [12] n answer kind (e.g. umber of det G. …”

Section: Self Consistencymentioning

confidence: 99%

Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Larsen

Shuryak

2015

Phys. Rev. D

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“…The most important factor affecting the good performance of the proposed algorithm is the use of an efficient algorithm for fast solving of eigenvalue problem (Cosnuau, 2014). Parallel computations were successfully implemented using the OpenMP programming interface.…”

Section: Summary and Practical Recommendationsmentioning

confidence: 99%

Estimation of structural stiffness with the use of Particle Swarm Optimization

Mazur

Galewski

Kaliński

2021

Lat. Am. j. solids struct.

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The paper presents the theoretical background and four applications examples of the new method for the estimation of support stiffness coefficients of complex structures modelled discretely (e.g. with the use of the Finite Element Model (FEM) method based on the modified Particle Swarm Optimization (PSO) algorithm. In real-life cases, exact values of the supports' stiffness coefficients may change for various reasons (e.g. order of fastening, state of the contact surfaces, environment changes, etc.). Because of the unknown coefficients, reliable simulations of fixed structure (i.e. mounted, assembled, not in a free-free state) are difficult to perform. The method serves as a tool to obtain good correlation between the FEM of a structure and the experimental data. Simple modal tests are required to estimate the first few modes of the fixed system. The FEM of the structure is considered in a free-free state and the support stiffness coefficients of the FEM are estimated by the proposed method. Further simulations with test-tuned and correlated complete FEM could be performed in time or frequency domain.

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“…Several works have been devoted to accelerate the computation for matrix calculations for many small matrices using GPUs [5,8,9,16]. Anderson et al [5] presented implementations of parallel computation of the LU decomposition and the QR decomposition for many small matrices on the GPU.…”

Section: Related Workmentioning

confidence: 99%

“…Dong et al [9] proposed a GPU implementation of the LU decomposition with pivoting for many dense matrices. Also, Cosnuau [8] proposed a GPU implementation of computing eigenvalues for many small matrices. However, the GPU implementation can compute eigenvalues only for Hermitian matrices.…”

Section: Related Workmentioning

confidence: 99%

An Efficient GPU Implementation of Bulk Computation of the Eigenvalue Problem for Many Small Real Non-symmetric Matrices

Tokura

Honda

Ito

et al. 2017

IJNC

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The main contribution of this paper is to present an efficient GPU implementation of bulk computation of eigenvalues for many small, non-symmetric, real matrices. This work is motivated by the necessity of such bulk computation in designing of control systems, which requires to compute the eigenvalues of hundreds of thousands non-symmetric real matrices of size up to 30 × 30. Several efforts have been devoted to accelerating the eigenvalue computation including computer languages, systems, environments supporting matrix manipulation offering specific libraries/function calls. Some of them are optimized for computing the eigenvalues of a very large matrix by parallel processing. However, such libraries/function calls are not aimed at accelerating the eigenvalues computation for a lot of small matrices. In our GPU implementation, we considered programming issues of the GPU architecture including warp divergence, coalesced access of the global memory, utilization of the shared memory, and so forth. In particular, we present two types of assignments of GPU threads to matrices and introduce three memory arrangements in the global memory. Furthermore, to hide CPU-GPU data transfer latency, overlapping computation on the GPU with the transfer is employed. Experimental results on NVIDIA TITAN X show that our GPU implementation attains a speed-up factor of up to 83.50 and 17.67 over the sequential CPU implementation and the parallel CPU implementation with eight threads on Intel Core i7-6700K, respectively.

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Computation on GPU of Eigenvalues and Eigenvectors of a Large Number of Small Hermitian Matrices

Cited by 19 publications

References 2 publications

Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Estimation of structural stiffness with the use of Particle Swarm Optimization

An Efficient GPU Implementation of Bulk Computation of the Eigenvalue Problem for Many Small Real Non-symmetric Matrices

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