This is an announcement for the paper "Least squares problems in orthornormalization" by Shanwen Hu.
Abstract: For any $n$-tuple $(\alpha_1,\cdots,\alpha_n)$ of linearly independent vectors in Hilbert space $H$, we construct a unique orthonormal basis $(\epsilon_1,\cdots,\epsilon_n)$ of $span{\alpha_1,\cdots,\alpha_n}$ satisfying: $$\sum_{i=1}^n|\epsilon_i-\alpha_i|^2\le\sum_{i=1}^n|\beta_i-\alpha_i|^2$$ for all orthonormal basis $(\beta_1,\cdots,\beta_n)$ of $span{\alpha_1,\cdots,\alpha_n}$. We study the stability of the orthornormalization and give some applications and examples.
Archive classification: math.FA
Remarks: 10 pages
Submitted from: swhu@math.ecnu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.7400
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