We provide a comparison between two schemes for solving equations on Banach space. A comparison between same convergence order schemes has been given using numerical examples which can go in favor of either scheme. However, we do not know in advance and under the same set of conditions which scheme has the largest ball of convergence, tighter error bounds or best information on the location of the solution. We present a technique that allows us to achieve this objective. Numerical examples are also given to further justify the theoretical results. Our technique can be used to compare other schemes of the same convergence order.

中文翻译：

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求解方程的两个三阶收敛阶方案之间的直接比较

我们提供了两种在Banach空间上求解方程的方案的比较。已经使用数值示例给出了相同收敛阶方案之间的比较，这可以有利于任一种方案。但是，我们不预先知道在相同的条件下哪种方案具有最大的收敛范围，更严格的误差范围或关于解决方案位置的最佳信息。我们提出了一种技术，可以实现这一目标。数值例子也为进一步证明理论结果辩护。我们的技术可以用来比较具有相同收敛阶数的其他方案。