期刊
LINEAR ALGEBRA AND ITS APPLICATIONS
卷 433, 期 7, 页码 1254-1264出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2010.06.031
关键词
Least squares; Bernstein-Vandermonde matrix; Bernstein basis; Bidiagonal decomposition; Total positivity
资金
- Spanish Government [MTM2009-07315]
The problem of polynomial least squares fitting in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix of the overdetermined system robe solved in the least squares sense is then a rectangular Bernstein-Vandermonde matrix. In order to use the method based on the QR decomposition of A, the first stage consists of computing the bidiagonal decomposition of the coefficient matrix A Starting from that bidiagonal decomposition, an algorithm for obtaining the QR decomposition of A is then applied. Finally, a triangular system is solved by using the bidiagonal decomposition of the R-factor of A. Some numerical experiments showing the behavior of this approach are included. (C) 2010 Elsevier Inc. All rights reserved
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