Implementation in Fpgas of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem

Bravo, Ignácio; Jiménez, Pedro Gil; Mazo, Manuel; Lázaro, José; Gardel, Alfredo

doi:10.1109/fpl.2006.311301

Cited by 34 publications

(14 citation statements)

References 2 publications

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“…These three parts can be integrated together by using multiplexers to select the data paths, as shown in Figure 4, where 2 adders, 2 shifters, and 4 multiplexers are required [5].…”

Section: Simplified -Rotation Cordicmentioning

confidence: 99%

“…Therefore, we must simplify the architecture in order to integrate more processors. A scaling-free -CORDIC for performing the plane rotation in (5) is used [5,6], where the number of inner iterations is reduced from 32 iterations to only one iteration.…”

Section: Simplified -Rotation Cordicmentioning

confidence: 99%

“…Therefore, as long as the algorithm's convergence properties are guaranteed, it is possible to adjust the architecture, which can significantly reduce the complexity with regard to the implementation. Computing the parallel eigenvalue decomposition (EVD) as a preprocessing step to MUSIC or ESPRIT algorithm with Jacobi's iterative method is used as an important example as the convergence of this method is extremely robust to modifications of the processor elements [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

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Parallel Jacobi EVD Methods on Integrated Circuits

2014

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Design strategies for parallel iterative algorithms are presented. In order to further study different tradeoff strategies in design criteria for integrated circuits, A 10 × 10 Jacobi Brent-Luk-EVD array with the simplified -CORDIC processor is used as an example. The experimental results show that using the -CORDIC processor is beneficial for the design criteria as it yields a smaller area, faster overall computation time, and less energy consumption than the regular CORDIC processor. It is worth to notice that the proposed parallel EVD method can be applied to real-time and low-power array signal processing algorithms performing beamforming or DOA estimation.

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“…These three parts can be integrated together by using multiplexers to select the data paths, as shown in Figure 4, where 2 adders, 2 shifters, and 4 multiplexers are required [5].…”

Section: Simplified -Rotation Cordicmentioning

confidence: 99%

Section: Simplified -Rotation Cordicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel Jacobi EVD Methods on Integrated Circuits

2014

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“…In Ahmedsaid et al [9], Liu et al [10] and Bravo et al [11], the target applications involve Principal Component Analysis (PCA) where the matrix size does not usually go over 20 × 20. The direct method of Jacobi [5] and its variants are used for these small eigenvalue problems.…”

Section: Related Workmentioning

confidence: 99%

“…Existing FPGA-based eigensolvers [9], [10] and [11] compute all the eigenvalues of very small matrices by using the direct method of Jacobi which has a computational complexity of Θ(n 3 ). We investigate a 2-stage iterative framework comprising the Lanczos method [5] followed by the bisection method [5] which has an overall computational complexity of Θ(n 2 ).…”

Section: Introductionmentioning

confidence: 99%

A High Throughput FPGA-Based Implementation of the Lanczos Method for the Symmetric Extremal Eigenvalue Problem

Rafique

Kapre

Constantinides

2012

Lecture Notes in Computer Science

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Abstract. Iterative numerical algorithms with high memory bandwidth requirements but medium-size data sets (matrix size ∼ a few 100s) are highly appropriate for FPGA acceleration. This paper presents a streaming architecture comprising floating-point operators coupled with highbandwidth on-chip memories for the Lanczos method, an iterative algorithm for symmetric eigenvalues computation. We show the Lanczos method can be specialized only for extremal eigenvalues computation and present an architecture which can achieve a sustained single precision floating-point performance of 175 GFLOPs on Virtex6-SX475T for a dense matrix of size 335×335. We perform a quantitative comparison with the parallel implementations of the Lanczos method using optimized Intel MKL and CUBLAS libraries for multi-core and GPU respectively. We find that for a range of matrices the FPGA implementation outperforms both multi-core and GPU; a speed up of 8.2-27.3× (13.4× geo. mean) over an Intel Xeon X5650 and 26.2-116× (52.8× geo. mean) over an Nvidia C2050 when FPGA is solving a single eigenvalue problem whereas a speed up of 41-520× (103× geo.mean) and 131-2220× (408× geo.mean) respectively when it is solving multiple eigenvalue problems.

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Signal Processing Architecture Implementation Methodologies for Next-Generation Remote Healthcare Systems

Acharyya

2013

Systems Design for Remote Healthcare

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Implementation in Fpgas of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem

Cited by 34 publications

References 2 publications

Parallel Jacobi EVD Methods on Integrated Circuits

Parallel Jacobi EVD Methods on Integrated Circuits

A High Throughput FPGA-Based Implementation of the Lanczos Method for the Symmetric Extremal Eigenvalue Problem

Signal Processing Architecture Implementation Methodologies for Next-Generation Remote Healthcare Systems

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