Abstract—

An algorithm for the numerical solution of Kepler’s equation with machine precision is presented. The convergence of the iterative sequence of Newton’s method is proved for the indicated initial approximation. The problem of finding a numerical solution to Kepler’s equation as a floating point number is formulated. Aspects related to computations near machine zero are taken into account. We analyzed the accuracy of the possible result. A problem is identified that arises when tending for the highest possible accuracy and a solution is proposed. An estimate is given of the computer time required to solve Kepler’s equation by this method.

中文翻译：

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开普勒方程的机器精度求解

摘要-

提出了一种具有机械精度的开普勒方程数值解的算法。对于指定的初始近似，证明了牛顿方法的迭代序列的收敛性。提出了寻找开普勒方程的数值解作为浮点数的问题。考虑到与机器零附近的计算有关的方面。我们分析了可能结果的准确性。确定了在寻求尽可能高的精度时出现的问题，并提出了解决方案。估计了用这种方法求解开普勒方程所需的计算机时间。