## Fast Algorithms for Computing Eigenvectors of Matrices via Pseudo Annihilating Polynomials. (arXiv:1811.09149v1 [math.NA])

An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as a variable. The algorithm, in principle, utilizes the minimal annihilating polynomials for eliminating redundant calculations. Furthermore, in the actual computation, the algorithm computes candidates of eigenvectors by utilizing pseudo annihilating polynomials and verifies their correctness. The experimental results show that our algorithms have better performance compared to conventional methods.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as a variable. The algorithm, in principle, utilizes the minimal annihilating polynomials for eliminating redundant calculations. Furthermore, in the actual computation, the algorithm computes candidates of eigenvectors by utilizing pseudo annihilating polynomials and verifies their correctness. The experimental results show that our algorithms have better performance compared to conventional methods.
﻿