抜粋
Max-plus algebra is a kind of idempotent semiring over Rmax:=R∪{−∞} with two operations ⊕:=max and ⊗:=+. In this paper, we introduce a new model of a walk on one dimensional lattice on Z, as an analogue of the quantum walk, over the max-plus algebra and we call it max-plus walk. In the conventional quantum walk, the summation of the ℓ2-norm of the states over all the positions is a conserved quantity. In contrast, the summation of eigenvalues of state decision matrices is a conserved quantity in the max-plus walk. Moreover, spectral analysis on the total time evolution operator is also given.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 29-48 |
| ページ数 | 20 |
| ジャーナル | Linear Algebra and Its Applications |
| 巻 | 598 |
| DOI | |
| 出版物ステータス | Published - 2020 8 1 |
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
フィンガープリント A walk on max-plus algebra' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。
これを引用
Watanabe, S., Fukuda, A., Segawa, E., & Sato, I. (2020). A walk on max-plus algebra. Linear Algebra and Its Applications, 598, 29-48. https://doi.org/10.1016/j.laa.2020.03.025