再论超松弛条件下的完全收敛迭代法
Finitely Convergent Iterative Methods with Overrelaxations Revisited
摘要：
研究了求解凸可行性问题的迭代法的有限收敛性。我们的关键假设是，内部的解决方案集是非空的，某些超松弛参数收敛到零，但速度慢于任何等比数列。与其他作品在这一领域，这需要发散级数的过度松弛，我们的方法允许我们考虑一些可求和的系列。通过采用准Fejérian分析在后一种情况下，我们得到额外的渐近收敛的保证，即使当内部的解决方案集是空的。
英文摘要：
We study the finite convergence of iterative methods for solving convex feasibility problems. Our key assumptions are that the interior of the solution set is nonempty and that certain overrelaxation parameters converge to zero, but with a rate slower than any geometric sequence. Unlike other works in this area, which require divergent series of overrelaxations, our approach allows us to consider some summable series. By employing quasi-Fejérian analysis in the latter case, we obtain additional asymptotic convergence guarantees, even when the interior of the solution set is empty.
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