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实际问题中往往只要求一个高阶矩阵的少量极端特征值。本文构造特殊位移使原来不按次序收敛的QL算法成为解决此类问题的有力手段。它避免了原有的方法的一些不足,与快速Givens方法结合可有效用于带状矩阵情况,对一般稀疏阵,本方法也能大大提高Lanczos算法的后期处理的效率。算法把按序收敛位移与Wilkinson位移结合以加速收敛进度,并给出了这种结合的转换时机的一个可计算性的条件。
In practical problems, only a small number of extreme eigenvalues of a higher-order matrix are often required. In this paper, we construct a special displacement to make QL algorithm, which is not convergent in the order, become a powerful method to solve such problems. It avoids some of the shortcomings of the original method, which can be effectively used in the case of banded matrix in combination with the fast Givens method. For the general thinned array, this method can also greatly improve the efficiency of post-processing of the Lanczos algorithm. The algorithm combines the order-dependent displacement with the Wilkinson shift to accelerate the convergence, and gives a computable condition for this combined transition.