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