A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems

Liao, Xia; Li, Shengguo; Lu, Yutong; Román, José E.

doi:10.1109/tpds.2020.3019471

Cited by 9 publications

(3 citation statements)

References 43 publications

(88 reference statements)

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“…The Divide-And-Conquer algorithm scales as

[ 43 ], where n is the matrix dimension. The steps used in the Divide-And-Conquer eigensolver are summarized in the following algorithm (Algorithm 1) flowchart [ 42 ].…”

Section: Theory and Methodologymentioning

confidence: 99%

GPU-Enhanced DFTB Metadynamics for Efficiently Predicting Free Energies of Biochemical Systems

et al. 2023

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Metadynamics calculations of large chemical systems with ab initio methods are computationally prohibitive due to the extensive sampling required to simulate the large degrees of freedom in these systems. To address this computational bottleneck, we utilized a GPU-enhanced density functional tight binding (DFTB) approach on a massively parallelized cloud computing platform to efficiently calculate the thermodynamics and metadynamics of biochemical systems. To first validate our approach, we calculated the free-energy surfaces of alanine dipeptide and showed that our GPU-enhanced DFTB calculations qualitatively agree with computationally-intensive hybrid DFT benchmarks, whereas classical force fields give significant errors. Most importantly, we show that our GPU-accelerated DFTB calculations are significantly faster than previous approaches by up to two orders of magnitude. To further extend our GPU-enhanced DFTB approach, we also carried out a 10 ns metadynamics simulation of remdesivir, which is prohibitively out of reach for routine DFT-based metadynamics calculations. We find that the free-energy surfaces of remdesivir obtained from DFTB and classical force fields differ significantly, where the latter overestimates the internal energy contribution of high free-energy states. Taken together, our benchmark tests, analyses, and extensions to large biochemical systems highlight the use of GPU-enhanced DFTB simulations for efficiently predicting the free-energy surfaces/thermodynamics of large biochemical systems.

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“…The Divide-And-Conquer algorithm scales as

[ 43 ], where n is the matrix dimension. The steps used in the Divide-And-Conquer eigensolver are summarized in the following algorithm (Algorithm 1) flowchart [ 42 ].…”

Section: Theory and Methodologymentioning

confidence: 99%

GPU-Enhanced DFTB Metadynamics for Efficiently Predicting Free Energies of Biochemical Systems

et al. 2023

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“…Their study showed that ADC can be three times faster than DC. On the other hand, Liao et al [82] proposed a parallel structured divideand-conquer aiming to reduce the computational cost. Their method builds the local matrices by employing Cauchylike matrix generators without any communication and then reduces the computation costs by utilizing a structured lowrank approximation method.…”

Section: Steganalysismentioning

confidence: 99%

Digital Image Steganalysis: Current Methodologies and Future Challenges

et al. 2022

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With the growing use of the internet and social media, data security has become a major issue. Thus, researchers are focusing on data security techniques such as steganography and steganalysis. Steganography is the approach of concealing the existence of secret messages in digital media for secure transmission. Steganalysis techniques aim to detect the existence of concealed messages and extract them. Digital image steganography and steganalysis techniques are classified into the spatial and transform domains. In this paper, we provide a detailed survey of the state-of-the-art works that have been performed in two-dimensional and three-dimensional image steganalysis. We present the most popular datasets and explain some steganographic methods for embedding hidden data. Steganalysis is a very difficult task due to the lack of information about the characteristics of the cover media that can be exploited to detect hidden messages. Therefore, we review studies performed on image steganalysis in the spatial and transform domains using classical machine learning and deep learning approaches. Additionally, we present open challenges and discuss some directions for future research.

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“…The DC algorithm [31] is easily parallelizable and has developed well in recent years [32,33]. However, efficient parallel implementations are not straightforward to program, and the decision to switch from task to data parallelism depends on the characteristics of the underlying machine.…”

Section: Introductionmentioning

confidence: 99%

A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem

2022

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The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a parallel computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate a single eigenvalue in parallel for now, especially in a specific order. This paper solves the issue with a new approach that can parallelize the Bisection iteration. Some pseudocodes and numerical results are presented. It shows our algorithm reduces the time cost by more than 35–70% compared to the Bisection algorithm while maintaining its accuracy and flexibility.

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A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems

Cited by 9 publications

References 43 publications

GPU-Enhanced DFTB Metadynamics for Efficiently Predicting Free Energies of Biochemical Systems

GPU-Enhanced DFTB Metadynamics for Efficiently Predicting Free Energies of Biochemical Systems

Digital Image Steganalysis: Current Methodologies and Future Challenges

A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem

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