Fast Algorithms for Computing Eigenvectors of Matrices via Pseudo Annihilating Polynomials
Provides a faster exact method for eigenvector computation, relevant to symbolic computation and numerical linear algebra communities.
The paper proposes an efficient exact algorithm for computing eigenvectors of integer matrices using pseudo annihilating polynomials, achieving better performance than conventional methods in experiments.
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.