FPGA implementation of complex-valued QR decomposition

Alhamed, Abdulrahman; Alshebeili, Saleh A.

doi:10.1109/icedsa.2016.7818557

Cited by 2 publications

(1 citation statement)

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“…As mentioned in the previous study [1], QR Algorithm [3] is chosen to work on asymmetric matrices. As a difference, the QR Decomposition structure in QR Algorithm is implemented using the Givens Rotation Principle [4] instead of Gram Schmidt Orthogonalization [5]. In both studies, the design is made using only basic mathematical modules and square root modules.…”

Section: Introductionmentioning

confidence: 99%

An FPGA Implementation of Givens Rotation Based Digital Architecture for Computing Eigenvalues of Asymmetric Matrix

Koseoglu

Ozturk

Ayhan

et al. 2021

2021 13th International Conference on Electrical and Electronics Engineering (ELECO)

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This paper proposes the digital circuit design that performs the eigenvalue calculation of asymmetric matrices with realvalued elements. Eigenvalues are computed iteratively through the QR algorithm. In the QR algorithm, the input matrix is factorized into orthogonal Q and upper triangular R matrix, then the RQ product is calculated to obtain an iterated matrix. For a time-efficient QR decomposition process, the Givens Rotation (GR) Principle is utilized to benefit from the parallelization feature. Parallelization is managed by the Systolic Array (SA) architecture that is created by placing Givens Generation (GG) and Row Updates (RU) blocks in a triangle array. In this paper, 4x4 input matrix is used to create a TSA architecture including n-1 diagonal (GG), and (n * (n-1)) / 2 off-diagonal (RU) modules. In the results section, Givens Rotation is compared with the Gram Schmidt algorithm used in our previous study [1] in terms of error, and area usage.

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