论文标题
框架近似与有界系数
Frame approximation with bounded coefficients
论文作者
论文摘要
由于它们的灵活性，希尔伯特空间的框架是近似方案中基地的有吸引力的替代品，对于识别基础不直接甚至可行的问题。但是，使用框架计算最佳近似可能会具有挑战性，因为它需要解决条件不良的线性系统。这种不良条件的结果是，这种框架近似的系数可以大大增长。在本文中，我们通过引入具有有限系数的框架近似方法来解决此问题。如我们所示，这些方法通常会导致近似准确性几乎没有或没有恶化，但成功地避免了以前方法固有的大系数，从而使它们在大系数不可取的情况下具有吸引力。我们还提出了理论分析以支持这些结论。
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames, however, can be challenging since it requires solving an ill-conditioned linear system. One consequence of this ill-conditioning is that the coefficients of such a frame approximation can grow large. In this paper we resolve this issue by introducing two methods for frame approximation that possess bounded coefficients. As we show, these methods typically lead to little or no deterioration in the approximation accuracy, but successfully avoid the large coefficients inherent to previous approaches, thus making them attractive in situations where large coefficients are undesirable. We also present theoretical analysis to support these conclusions.
