This paper proposes a Newton type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equations associated to this problem, we construct a sequence which converges quadratically towards the solution. This construction is not based on the resolution of linear system as it is the case in the classical Newton method. Moreover, we provide a theoretical analysis of this construction to exhibit a condition to get a quadratic convergence. We also propose numerical experiments, which illustrate the theoretical results. This shows that classical QR method would gain in efficiency incorporating the tests given by the theory.

翻译：本文建议了一种牛顿型方法, 以数字方式解决数种可分解的矩阵的二元问题, 这些矩阵是双向通勤的。 经典结果显示这些矩阵同时可以对等化。 我们从与这一问题相关的一个适当的方程式系统中, 构建了一个将二次相交的序列。 这个构造不是基于线性系统的分辨率, 正如古典牛顿法那样 。 此外, 我们对这一构造进行理论分析, 以展示获得二次趋同的条件 。 我们还提出数字实验, 以说明理论结果 。 这显示经典的 QR 方法将提高效率, 将理论给出的测试纳入其中 。