## On computing maximum/minimum singular values of a generalized tensor sum

Asuka Ohashi and Tomohiro Sogabe

### Abstract

We consider the efficient computation of the maximum/minimum singular values of a generalized tensor sum $T$. The computation is based on two approaches: first, the Lanczos bidiagonalization method is reconstructed over tensor space, which leads to a memory-efficient algorithm with a simple implementation, and second, a promising initial guess given in Tucker decomposition form is proposed. From the results of numerical experiments, we observe that our computation is useful for matrices being near symmetric, and it has the potential of becoming a method of choice for other cases if a suitable core tensor can be given.

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### Key words

generalized tensor sum, Lanczos bidiagonalization method, maximum and minimum singular values

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