Diagonalization of tensors with circulant structure |
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| Authors: | Mansoor Rezghi |
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| Institution: | a Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran
b Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden |
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| Abstract: | The concepts of tensors with diagonal and circulant structure are defined and a framework is developed for the analysis of such tensors. It is shown a tensor of arbitrary order, which is circulant with respect to two particular modes, can be diagonalized in those modes by discrete Fourier transforms. This property can be used in the efficient solution of linear systems involving contractive products of tensors with circulant structure. Tensors with circulant structure occur in models for image blurring with periodic boundary conditions. It is shown that the new framework can be applied to such problems. |
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| Keywords: | Tensor Diagonal tensor Circulant structure Discrete Fourier transform Image blurring model Periodic boundary conditions Preconditioner |
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