Abstract Given a finite sequence of vectors in a finite dimensional Hilbert space, we present a method to obtain a tight frame by appending some vectors with prescribed norms. The approach, based on the alternating projection technique, is an iterative process. Von Neumann trace inequality and the polar decomposition of the matrix are employed to derive the method. The approach can be easily implemented and is numerically stable. The local convergence of the approach is achieved. Numerical examples are given to show the performance of the method.

中文翻译：

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通过交替投影方法按规定规范完成帧

摘要 给定有限维希尔伯特空间中的有限向量序列，我们提出了一种通过附加一些具有规定范数的向量来获得紧框架的方法。该方法基于交替投影技术，是一个迭代过程。使用冯诺依曼迹不等式和矩阵的极分解来推导该方法。该方法很容易实现并且在数值上是稳定的。实现了该方法的局部收敛。给出了数值例子来说明该方法的性能。