论文标题
使用无限许多子空间同时投影的方法的错误界限
Error Bounds for the Method of Simultaneous Projections with Infinitely Many Subspaces
论文作者
论文摘要
我们研究了实际希尔伯特空间的许多封闭和线性子空间应用于同时投影方法的性质。我们建立了该方法线性收敛的最佳误差，我们根据在无限乘积空间中计算的弗里德里奇角的余弦表示。此外，我们为上述数字提供估计和替代表达式。此外，我们将此数字与二分法定理联系起来，并将其与超多个快速的快速收敛相关联。我们还讨论了针对特别选择的起点进行的同时投影方法的多项式收敛。
We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method, which we express in terms of the cosine of the Friedrichs angle computed in an infinite product space. In addition, we provide estimates and alternative expressions for the above-mentioned number. Furthermore, we relate this number to the dichotomy theorem and to super-polynomially fast convergence. We also discuss polynomial convergence of the simultaneous projection method which takes place for particularly chosen starting points.
