Implementing the Jacobi Algorithm for Solving Eigenvalues of Symmetric Matrices with CUDA

Wang, Tao; Guo, Lei; Li, Guilin; Li, Jinbao; Wang, Renda; Ren, Meirui; He, Jing

doi:10.1109/nas.2012.12

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…In combination of (3.1) and (3.3), which is mentioned in the Chapter 3, eigenvalues for a general matrix with CUDA can be determined. This goal requested in [28] using QR method as the future work and in this thesis we have reached to first part of this procedure with outstanding results.…”

Section: Comparisonmentioning

confidence: 99%

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Acceleration of Hessenberg reduction for nonsymmetric matrix

Nekouei¹

2023

Preprint

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The worth of finding a general solution for nonsymmetric eigenvalue problems is specified in many areas of engineering and science computations, such as reducing noise to have a quiet ride in automotive industrial engineering or calculating the natural frequency of a bridge in civil engineering. The main objective of this thesis is to design a hybrid algorithm (based on CPU-GPU) in order to reduce general non-symmetric matrices to Hessenberg form. A new blocks method is used to achieve great efficiency in solving eigenvalue problems and to reduce the execution time compared with the most recent related works. The GPU part of proposed algorithm is thread based with asynchrony structure (based on FFT techniques) that is able to maximize the memory usage in GPU. On a system with an Intel Core i5 CPU and NVIDA GeForce GT 635M GPU, this approach achieved 239.74 times speed up over the CPU-only case when computing the Hessenberg form of a 256 * 256 real matrix. Minimum matrix order (n), which the proposed algorithm supports, is sixteen. Therefore, supporting this matrix size is led to have the large matrix order range.

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Section: Comparisonmentioning

confidence: 99%

“…CUDA was used for accelerating the reduction to upper hessenberg forms and solving eigenvalues problems [2,28]. They used BLAS library for matrix-matrix and vector-matrix implementation.…”

Section: Literature Surveymentioning

confidence: 99%

Acceleration of Hessenberg reduction for nonsymmetric matrix

Nekouei¹

2023

Preprint

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“…Since this process is iterative and strongly dependent on the previous iterations data, several experiments revealed that the GPU paradigm is not able to accelerate the algorithm with such a reduced number of bands [40]. Therefore, and taking into account that no memory copies are needed between CPU and GPU, this process has been developed in the CPU.…”

Section: C: Jacobimentioning

confidence: 99%

Parallel Implementations Assessment of a Spatial-Spectral Classifier for Hyperspectral Clinical Applications

et al. 2019

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Hyperspectral (HS) imaging presents itself as a non-contact, non-ionizing and non-invasive technique, proven to be suitable for medical diagnosis. However, the volume of information contained in these images makes difficult providing the surgeon with information about the boundaries in real-time.To that end, High-Performance-Computing (HPC) platforms become necessary. This paper presents a comparison between the performances provided by five different HPC platforms while processing a spatialspectral approach to classify HS images, assessing their main benefits and drawbacks. To provide a complete study, two different medical applications, with two different requirements, have been analyzed. The first application consists of HS images taken from neurosurgical operations; the second one presents HS images taken from dermatological interventions. While the main constraint for neurosurgical applications is the processing time, in other environments, as the dermatological one, other requirements can be considered. In that sense, energy efficiency is becoming a major challenge, since this kind of applications are usually developed as hand-held devices, thus depending on the battery capacity. These requirements have been considered to choose the target platforms: on the one hand, three of the most powerful Graphic Processing Units (GPUs) available in the market; and, on the other hand, a low-power GPU and a manycore architecture, both specifically thought for being used in battery-dependent environments.INDEX TERMS Hyperspectral imaging, high performance computing, parallel processing, parallel architectures, image processing, biomedical engineering, medical diagnostic imaging, cancer detection, supervised classification, support vector machines, K-nearest neighbors, principal component analysis, graphic processing unit, manycore.

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GPU Acceleration of Finding Maximum Eigenvalue of Positive Matrices

Tian

Guo

et al. 2014

Algorithms and Architectures for Parallel Processing

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Implementing the Jacobi Algorithm for Solving Eigenvalues of Symmetric Matrices with CUDA

Cited by 6 publications

References 8 publications

Acceleration of Hessenberg reduction for nonsymmetric matrix

Acceleration of Hessenberg reduction for nonsymmetric matrix

Parallel Implementations Assessment of a Spatial-Spectral Classifier for Hyperspectral Clinical Applications

GPU Acceleration of Finding Maximum Eigenvalue of Positive Matrices

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