Generation of finite tight frames by Householder transformations |
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| Authors: | De-Jun Feng Long Wang Yang Wang |
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| Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China;(2) Mathematics Department, Southern Polytechnic State University, Mariieta, GA, 30060, U.S.A.;(3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, U.S.A. |
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| Abstract: | 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 ?n or ?n only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ?n or ?n, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame? |
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| Keywords: | frames tight frame tight frame matrix Householder matrix condition number |
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