无限多子空间同时投影法的误差界
Error Bounds for the Method of Simultaneous Projections with Infinitely Many Subspaces
摘要：
研究了实希尔伯特空间中可数无穷多个闭线性子空间的同时投影方法的性质。我们建立了这种方法的线性收敛的最佳误差界，我们表示在无穷乘积空间中计算的Friedrichs角的余弦。此外，我们提供了上述数字的估计和替代表达式。此外，我们将这个数字的二分法定理和超多项式快速收敛。我们还讨论了多项式收敛的同时投影方法发生特别选择的起点。
英文摘要：
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.
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