T. Sakata

activity

20082018

most citedRank of 3-tensors with 2 slices and Kronecker canonical forms

16 citations · 33 across the 14 of their papers we have counts for

collaborators

14 papers

math.RA2018

Maximal and typical nonnegative ranks of nonnegative tensors

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Let $N_{1}, \dots, N_{d}$ be positive integers with $N_{1} \leq \dots \leq N_{d}$ . Set $N = N_{1} \dots N_{d - 1}$ . We show in this paper that an integer $r$ is a typical nonnegative rank of nonn…

math.RA2017

Typical ranks of semi-tall real 3-tensors

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Let $m$ , $n$ and $p$ be integers with $3 \leq m \leq n$ and $(m - 1) (n - 1) + 1 \leq p \leq (m - 1) m$ . We showed in previous papers that if $p \geq (m - 1) (n - 1) + 2$ , then typical ranks of $p\times…

math.RA2015

Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Let $m, n \geq 3$ , $(m - 1) (n - 1) + 2 \leq p \leq mn$ , and $u = mn - p$ . The set $R^{u \times n \times m}$ of all real tensors with size $u \times n \times m$ is one to one corresponding t…

stat.CO2013

Holonomic Decent Minimization Method for Restricted Maximum Likelihood Estimation

Rieko Sakurai, Toshio Sakata

Recently, the school of Takemura and Takayama have developed a quite interesting minimization method called holonomic gradient descent method (HGD). It works by a mixed use of Pfaf…

math.RA2013★ 2 cited

Rank of tensors with size 2 x ... x 2

Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki

We study an upper bound of ranks of $n$ -tensors with size $2 \times \dots \times 2$ over the complex and real number field. We characterize a $2 \times 2 \times 2$ tensor with rank 3 by…

math.RA2013★ 1 cited

Upper bound of typical ranks of m x n x ((m-1)n-1) tensors over the real number field

Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki

Let $3 \leq m \leq n$ . We study typical ranks of $m \times n \times ((m - 1) n - 1)$ tensors over the real number field. The number $(m - 1) n - 1$ is a minimal typical rank of $m\times n\times…