We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses complex moments to extract the eigencomponents of interest from a random matrix and uses the Rayleigh--Ritz procedure to project a given eigenvalue problem into a reduced eigenvalue problem. The complex moment is given by contour integral and approximated by using numerical quadrature. We split the error in the complex moment into the truncation error of the quadrature and rounding errors and evaluate each. This idea for error evaluation inherits our previous Hankel matrix approach, whereas the proposed method requires half the number of quadrature points for the previous approach to reduce the truncation error to the same order. Moreover, the Rayleigh--Ritz procedure approach forms a transformation matrix that enables verification of the eigenvectors. Numerical experiments show that the proposed method is faster than previous methods while maintaining verification performance.

翻译：我们提出一个区域中的乙基值的核查计算方法,以及泛泛的赫米蒂亚的乙基值问题的相应向量计算器。拟议方法使用复杂的时间从随机矩阵中提取有兴趣的乙基成分,并使用雷利利-里兹程序将给定的乙基值问题投射成一个减少的乙基值问题。复杂的时刻由等离子整体给出,并使用数字二次曲线进行近似。我们将复杂时刻的错误分为二次和四舍五入误差,并对每个误差进行评估。这种误差评价的想法继承了我们先前的汉克尔矩阵方法,而拟议方法则要求将先前方法的二次曲线误差减少一半。此外,雷利-里兹程序方法形成了一个能够核查乙基体的变异矩阵。Numerical实验表明,在保持核查性能的同时,拟议的方法比以前的方法要快。