An Exact Algorithm for Computing the Structure of Jordan Blocks

📝 Original Info

• Title: An Exact Algorithm for Computing the Structure of Jordan Blocks
• ArXiv ID: 2510.03103
• Date: 2025-10-03
• Authors: Shinichi Tajima, Katsuyoshi Ohara, Akira Terui

📝 Abstract

An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However, for deriving just the structure of Jordan chains, the algorithm can be reduced to increase its efficiency. We propose a modification of the algorithm for that purpose. Results of numerical experiments are given.

💡 Deep Analysis

This research explores the key findings and methodology presented in the paper: An Exact Algorithm for Computing the Structure of Jordan Blocks.

An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However, for deriving just the structure of Jordan chains, the algorithm can be reduced to increase its efficiency. We propose a modification of the algorithm for that purpose. Results of numerical experiments are given.

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