关键词: 对称张量, 特征对, 可信性验证, 牛顿法

Abstract: By using the inversefree Newton’s method and the interval algorithm theory, we studied the credibility verification of Z-eigenpairs of symmetric tensors, and proposed an interval algorithm to calculate Z-eigenpairs. The algorithm output an approximate Z-eigenpair and its corresponding error bound, so that an exact Z-eigenpair of symmetric tensors must exist within the error range of the approximate solution.

Key words: symmetric tensor, eigenpairs, credibility verification, Newton’s method