Finding a feasible point that satisfies a set of constraints is a common task in scientific computing: examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems; an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice it usually converges faster than ART3 does. In this paper we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (i) finite convergence is retained and (ii) the speed of convergence is improved. The first of these two properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem.

中文翻译：

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有限收敛序列算法的有效控制。

寻找满足一组约束的可行点是科学计算中的一项常见任务：示例是线性可行性问题和凸可行性问题。有限收敛序列算法可用于解决此类问题；这种算法的一个例子是 ART3，它以这样一种方式定义，即它的控制是循环的，在它的执行过程中，它重复循环通过给定的约束。之前我们发现了 ART3 的一个变体，它的控制不再是循环的，但它仍然是有限收敛的，实际上它通常比 ART3 收敛得更快。在本文中，我们提出了一种用于有限收敛序列算法自动转换的通用方法，其方式是 (i) 保留有限收敛和 (ii) 提高收敛速度。