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2016•Linear and Multilinear AlgebraRequires access

A fast algorithm for solving circulant tensor systems

Ze-Jia Xie, Xiaoqing Jin, Yimin Wei

Open publisher page 17 citations

Abstract

A new definition for circulant tensors is given, which is a generalization of the one for circulant matrices. Furthermore, we define the generalized circulant tensors which can be diagonalized by the Fourier matrix F and/or . We also consider solving the circulant tensor systems by a fast algorithm based on the fast Fourier transform (FFT). Such algorithm is similar to that for circulant linear systems and it can also be performed in .

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What this paper is about

A new definition for circulant tensors is given, which is a generalization of the one for circulant matrices. Furthermore, we define the generalized circulant tensors which can be diagonalized by the Fourier matrix F and/or . We also consider solving the circulant tensor systems by a fast algorithm based on the fast Fourier transform (FFT). Such algorithm is similar to that for circulant linear systems and it can also be performed in .

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OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A new definition for circulant tensors is given, which is a generalization of the one for circulant matrices. Furthermore, we define the generalized circulant tensors which can be diagonalized by the Fourier matrix F and/or . We also consider solving the circulant tensor systems by a fast algorithm based on the fast Fourier transform (FFT). Such algorithm is similar to that for circulant linear systems and it can also be performed in .

Key concepts: Circulant matrix, Fast Fourier transform, Mathematics, Generalization, Tensor (intrinsic definition), Matrix (chemical analysis), Algorithm, Algebra over a field

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