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

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Abstract

Field-programmable gate arrays (FPGAs) are one attractive hardware platform for computing the eigenvalue decomposition of low-dimensional symmetric matrices. For this, one popular method is using the parallel Jacobi algorithm based on coordinate rotations digital computer (CORDIC). We here present a novel efficient FPGA architecture for computing the eigenvalue decomposition, whose main idea is from the fact that rotation matrices in Jacobi’s method belong to a category of special sparse matrices. Based on the above characteristic, matrix multiplications in the parallel Jacobi algorithm can be performed by FPGA efficiently. In addition, we provide one solution for Jacobi’s method to decompose the complex Hermitian matrix. Then, our proposed design is compared with state-of-the-arts on one Xilinx XC7V690T FPGA. Due to the high real-time requirement, we finally take the subspace-based direction of arrival (DOA) estimation in wireless communication as an application example.

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We provide one MATLAB demo to illustrate the performance of our proposed method in this paper, which are available for the readers. Meanwhile, this demo is also available from the corresponding author on request.

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Acknowledgements

The authors acknowledge the support of science research project of department of transport of Shaanxi province in 2020: research and application of refined maintenance evaluation and decay model based on 3D pavement (No. 20-24K).

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Correspondence to Wei-Xing Wang.

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Yan, D., Wang, WX. & Zhang, XW. High-Performance Matrix Eigenvalue Decomposition Using the Parallel Jacobi Algorithm on FPGA. Circuits Syst Signal Process 42, 1573–1592 (2023). https://doi.org/10.1007/s00034-022-02180-7

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