High Level Synthesis FPGA Implementation of the Jacobi Algorithm to Solve the Eigen Problem

Bravo, Ignácio; Vázquez, C. Martínez; Gardel, Alfredo; Lázaro, José; Palomar, Esther

doi:10.1155/2015/870569

Cited by 13 publications

(3 citation statements)

References 22 publications

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“…For Hermitian matrices, which is the case of R Y , algorithms that are mostly used are the QR algorithm (for matrices with order m ≤ 25) [12], and the Lanczos algorithm (for moderated-to-high values of m, less than a few thousands) [11], [13]. The Jacobi algorithm is another well-known alternative; it has been considered in microchip implementations [14] in the context of eigenvalue-based spectrum sensing [15].…”

Section: B Problem Descriptionmentioning

confidence: 99%

Performance of Eigenvalue-Based Spectrum Sensing With Approximate Eigenvalue Estimation Methods

Guimarães¹,

Aquino²,

Santos³

et al. 2019

JCIS

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This article presents a performance and computational run-time analysis of cooperative spectrum sensing techniques based on the eigenvalues of the received signal sample covariance matrix, under three methods for approximate eigenvalue estimation: the Cholesky iterations algorithm, the Gershgorin theorem with transformed covariance matrix, and the conventional Gershgorin theorem. Widely used eigenvaluebased test statistics are addressed: the generalized likelihood ratio test, the ratio between the maximum and the minimum eigenvalues, and the Roy's largest root test. Simulation results show that the first two eigenvalue estimation methods can yield comparable performances, whereas the latter may operate satisfactorily only in situations of high signal-to-noise ratios. It is also demonstrated that the test statistics are not equally sensitive to eigenvalue estimation errors. The Cholesky iterations algorithm is attractive in terms of run-time and performance for all spectrum sensing techniques, while the simple Gershgoring method may be attractive for the Roy's largest root test.

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Section: B Problem Descriptionmentioning

confidence: 99%

Performance of Eigenvalue-Based Spectrum Sensing With Approximate Eigenvalue Estimation Methods

Guimarães¹,

Aquino²,

Santos³

et al. 2019

JCIS

View full text Add to dashboard Cite

show abstract

“…In recent years, there has been intense interest for emerging applications in embedded systems, such as multiple-input multiple-output (MIMO) systems [36,37], data analytics [38][39][40][41], sparse representation of signals [42][43][44][45][46][47], that require efficient SVD algorithms. Since SVD algorithms reduce to solve an eigenvalue problem, that is computationally expensive, both specific hardware solutions [48][49][50][51][52][53][54][55][56] and parallel implementations [57,58] have been proposed to overcome this bottleneck.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding more complex architectures, there is a rich literature on how to implement mathematical algorithms on Field Programmable Gate Arrays (FPGAs) and other programmable hardware [53][54][55][56]. Those are generally sophisticated and expensive systems, used for high-end applications and exploiting a completely different computation model, based on massive parallelism.…”

Section: Introductionmentioning

confidence: 99%

Singular Value Decomposition in Embedded Systems Based on ARM Cortex-M Architecture

et al. 2020

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Singular value decomposition (SVD) is a central mathematical tool for several emerging applications in embedded systems, such as multiple-input multiple-output (MIMO) systems, data analytics, sparse representation of signals. Since SVD algorithms reduce to solve an eigenvalue problem, that is computationally expensive, both specific hardware solutions and parallel implementations have been proposed to overcome this bottleneck. However, as those solutions require additional hardware resources that are not in general available in embedded systems, optimized algorithms are demanded in this context. The aim of this paper is to present an efficient implementation of the SVD algorithm on ARM Cortex-M. To this end, we proceed to (i) present a comprehensive treatment of the most common algorithms for SVD, providing a fairly complete and deep overview of these algorithms, with a common notation, (ii) implement them on an ARM Cortex-M4F microcontroller, in order to develop a library suitable for embedded systems without an operating system, (iii) find, through a comparative study of the proposed SVD algorithms, the best implementation suitable for a low-resource bare-metal embedded system, (iv) show a practical application to Kalman filtering of an inertial measurement unit (IMU), as an example of how SVD can improve the accuracy of existing algorithms and of its usefulness on a such low-resources system. All these contributions can be used as guidelines for embedded system designers. Regarding the second point, the chosen algorithms have been implemented on ARM Cortex-M4F microcontrollers with very limited hardware resources with respect to more advanced CPUs. Several experiments have been conducted to select which algorithms guarantee the best performance in terms of speed, accuracy and energy consumption.

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High-Performance Matrix Eigenvalue Decomposition Using the Parallel Jacobi Algorithm on FPGA

Yan

Wang

Zhang

2022

Circuits Syst Signal Process

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High Level Synthesis FPGA Implementation of the Jacobi Algorithm to Solve the Eigen Problem

Cited by 13 publications

References 22 publications

Performance of Eigenvalue-Based Spectrum Sensing With Approximate Eigenvalue Estimation Methods

Performance of Eigenvalue-Based Spectrum Sensing With Approximate Eigenvalue Estimation Methods

Singular Value Decomposition in Embedded Systems Based on ARM Cortex-M Architecture

High-Performance Matrix Eigenvalue Decomposition Using the Parallel Jacobi Algorithm on FPGA

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