Generation of finite tight frames by Householder transformations
Generation of finite tight frames by Householder transformations
复制标题
通过 Householder 变换生成有限紧框架
DOI：
10.1007/s10444-004-7637-9
复制
发表时间：
2006
影响因子：
1.7
通讯作者：
Yang Wang
中科院分区：
文献类型：
--
作者：
De;Long Wang;Yang Wang
有限紧框架被广泛应用于许多领域。一个重要的问题是对紧框架中的每个向量构造具有给定范数的有限框架。在本文中，我们提供了一个快速，简单的算法，这样的目的。我们的算法采用Householder变换。对于m个向量组成的有限紧框架，只需O（nm）的运算。此外，我们还研究了下面的问题：给定一组向量在n或n中，有多少额外的向量，可能与约束，需要添加，以获得一个紧框架？
Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝn or ℂn only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝn or ℂn, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame?