caa a22 4500 46793925X CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7637-9 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7637-9 Generation of finite tight frames by Householder transformations [Elektronische Daten] [De-Jun Feng, Long Wang, Yang Wang] 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? Springer, 2006 frames nationallicence tight frame nationallicence tight frame matrix nationallicence Householder matrix nationallicence condition number nationallicence Feng De-Jun Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut Wang Long Mathematics Department, Southern Polytechnic State University, 30060, Mariieta, GA, U.S.A. aut Wang Yang School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, U.S.A. aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 297-309 1019-7168 24:1-4<297 2006 24 10444 https://doi.org/10.1007/s10444-004-7637-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7637-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feng De-Jun Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut NATIONALLICENCE 700 1- Wang Long Mathematics Department, Southern Polytechnic State University, 30060, Mariieta, GA, U.S.A aut NATIONALLICENCE 700 1- Wang Yang School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, U.S.A aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 297-309 1019-7168 24:1-4<297 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer