Tensor-Tensor Product Toolbox

06/17/2018

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by   Canyi Lu, et al.

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Tensors are higher-order extensions of matrices. In recent work [Kilmer and Martin, 2011], the authors introduced the notion of the t-product, a generalization of matrix multiplication for tensors of order three. The multiplication is based on a convolution-like operation, which can be implemented efficiently using the Fast Fourier Transform (FFT). Based on t-product, there has a similar linear algebraic structure of tensors to matrices. For example, there has the tensor SVD (t-SVD) which is computable. By using some properties of FFT, we have a more efficient way for computing t-product and t-SVD in [C. Lu, et al., 2018]. We develop a Matlab toolbox to implement several basic operations on tensors based on t-product. The toolbox is available at https://github.com/canyilu/tproduct.