The cyclic Jacobi method for computing the principal values of a complex matrix

Forsythe, George E.; Henrici, Péter

doi:10.1090/s0002-9947-1960-0109825-2

Cited by 194 publications

(102 citation statements)

References 13 publications

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“…Different iterative methods have been described in the literature [17]. Among them, the Jacobi method [18][19][20] is distinguished. In this method, the sequential nature of the iterative process is balanced with the possibility to exploit its inherent parallelism.…”

Section: Introductionmentioning

confidence: 99%

Implementation of the Principal Component Analysis onto High-Performance Computer Facilities for Hyperspectral Dimensionality Reduction: Results and Comparisons

et al. 2018

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Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal Component Analysis (PCA), suffer from their computationally demanding nature, becoming advisable for their implementation onto high-performance computer architectures for applications under strict latency constraints. This work presents the implementation of the PCA algorithm onto two different high-performance devices, namely, an NVIDIA Graphics Processing Unit (GPU) and a Kalray manycore, uncovering a highly valuable set of tips and tricks in order to take full advantage of the inherent parallelism of these high-performance computing platforms, and hence, reducing the time that is required to process a given hyperspectral image. Moreover, the achieved results obtained with different hyperspectral images have been compared with the ones that were obtained with a field programmable gate array (FPGA)-based implementation of the PCA algorithm that has been recently published, providing, for the first time in the literature, a comprehensive analysis in order to highlight the pros and cons of each option.

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Section: Introductionmentioning

confidence: 99%

Implementation of the Principal Component Analysis onto High-Performance Computer Facilities for Hyperspectral Dimensionality Reduction: Results and Comparisons

et al. 2018

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“…The first proof of convergence of the CJT for complex Hermitian matrices was given in [6]. However, this result did not determine the convergence rate.…”

Section: The One-bit Blind Null Space Learning Algorithm (Obnsla)mentioning

confidence: 99%

“…The indices (l k , m k ) are chosen as in the CJT. After performing k s iterations the SU approximates the matrix V (see (6)) by W ks . It then chooses its pre-coding matrix T ks as Although the SU becomes "invisible" to the PU after it learns N (H ps ), it interferes with the PU during this learning process.…”

Section: B the Obnslamentioning

confidence: 99%

One-Bit Null Space Learning for MIMO underlay cognitive radio

Noam

Goldsmith

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-We present a new algorithm, called the One-Bit Null Space Learning Algorithm (OBNSLA), for MIMO cognitive radio Secondary Users (SU) to learn the null space of the interference channel to the Primary User (PU). The SU observes a binary function that indicates whether the interference it inflicts on the PU has increased or decreased in comparison to the SU's previous transmitted signal. This function is obtained by listening to the PU's transmitted signal or control channel and extracting information from it about whether the PU's Signal to Interference plus Noise power Ratio has increased or decreased. In addition to introducing the OBNSLA, the paper provides a thorough convergence analysis of this algorithm. The OBNSLA is shown to have a linear convergence rate and an asymptotic quadratic convergence rate.

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“…The computational burden on BSFA and LEM is the one time cost of matrix eigendecomposition, which has cubic complexity [7]. SFA uses covariance matrices of sensory input, which scale with input dimension I.…”

Section: Computational Complexity Space Complexitymentioning

confidence: 99%

Low Complexity Proto-Value Function Learning from Sensory Observations with Incremental Slow Feature Analysis

Luciw

Schmidhuber

2012

Artificial Neural Networks and Machine Learning – ICANN 2012

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Abstract. We show that Incremental Slow Feature Analysis (IncSFA) provides a low complexity method for learning Proto-Value Functions (PVFs). It has been shown that a small number of PVFs provide a good basis set for linear approximation of value functions in reinforcement environments. Our method learns PVFs from a high-dimensional sensory input stream, as the agent explores its world, without building a transition model, adjacency matrix, or covariance matrix. A temporaldifference based reinforcement learner improves a value function approximation upon the features, and the agent uses the value function to achieve rewards successfully. The algorithm is local in space and time, furthering the biological plausibility and applicability of PVFs.

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The cyclic Jacobi method for computing the principal values of a complex matrix

Cited by 194 publications

References 13 publications

Implementation of the Principal Component Analysis onto High-Performance Computer Facilities for Hyperspectral Dimensionality Reduction: Results and Comparisons

Implementation of the Principal Component Analysis onto High-Performance Computer Facilities for Hyperspectral Dimensionality Reduction: Results and Comparisons

One-Bit Null Space Learning for MIMO underlay cognitive radio

Low Complexity Proto-Value Function Learning from Sensory Observations with Incremental Slow Feature Analysis

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