Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ghost-OSD Method on Numerical Max-Plus Algebra

Yohei Oshida

TL;DR

Ghost-OSD Method that can quickly calculate the powers of honest matrix is explained that can reduce the calculation time of matrix exponentiation calculations on numerical max-plus algebra.

Abstract

In this paper, we introduce a method for reducing the calculation time of matrix exponentiation calculations on numerical max-plus algebra. In particular, we explain Ghost-OSD Method that can quickly calculate the powers of honest matrix. For more information on this abstract, see the PDF.

Ghost-OSD Method on Numerical Max-Plus Algebra

TL;DR

Ghost-OSD Method that can quickly calculate the powers of honest matrix is explained that can reduce the calculation time of matrix exponentiation calculations on numerical max-plus algebra.

Abstract

In this paper, we introduce a method for reducing the calculation time of matrix exponentiation calculations on numerical max-plus algebra. In particular, we explain Ghost-OSD Method that can quickly calculate the powers of honest matrix. For more information on this abstract, see the PDF.
Paper Structure (7 sections, 10 theorems, 143 equations, 6 figures)

This paper contains 7 sections, 10 theorems, 143 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Proof
  3. Computation Speed Analysis
  4. The case of Theorem $\ref{['Main']}$
  5. The case of Theorem $\ref{['main']}$
  6. Conclusion.
  7. Bounus : Jet Black Theorem , Elementary cellular automaton and Oshida Rule

Key Result

Theorem 1.1

On the calculation of $X(k)$ for $k=1,2,\cdots,2m,\cdots$, we can shorten the number of calculations of $X(k)$ by following steps $(1)$ to $(5)$ below. $(1)$Let us denote and Then, for $k=1,2,\cdots,m-1$, we have for each i. $(2)$For $k=m,m+1,\cdots,2m-1$, we can compute as follows. $(3)$For $k=2m$, we can compute as follows: $(4)$Let $\alpha \in \mathbb{Z}_{>1}$ and $\beta$ be the non-negati

Figures (6)

  • Figure :
  • Figure :
  • Figure :
  • Figure :
  • Figure :
  • ...and 1 more figures

Theorems & Definitions (27)

  • Theorem 1.1: Ghost-OSD Method
  • Theorem 1.2
  • Definition 2.1: Support of vector and matrix
  • Example 2.2
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • Lemma 2.5
  • proof
  • Corollary 2.6
  • ...and 17 more