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Volume 10, Issue 1
Solution of an Overdetermined System of Linear Equations in $L_2$, $L_∞$, $L_P$ Norm Using L.S. Techniques

Shu-Guang Yang & Jian-Wen Liao

J. Comp. Math., 10 (1992), pp. 29-38.

Published online: 1992-10

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  • Abstract

A lot of curve fitting problems of experiment data lead to solution of an overdetermined system of linear equations. But it is not clear prior to that whether the data are exact or contaminated with errors of an unknown nature. Consequently we need to use not only $L_2$-solution of the system but also $L_{\infty}$- or $L_p$-solution.
In this paper, we propose a universal algorithm called the Directional Perturbation Least Squares (DPLS) Algorithm, which can give optimal solutions of an overdetermined system of linear equations in $L_2$, $L_{\infty}$,$L_p (1\leq p＜2)$ norms using only L.S. techniques (in $\S$2). Theoretical principle of the algorithm is given in $\S$ 3. Two examples are given in the end.  

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@Article{JCM-10-29, author = {Yang , Shu-Guang and Liao , Jian-Wen}, title = {Solution of an Overdetermined System of Linear Equations in $L_2$, $L_∞$, $L_P$ Norm Using L.S. Techniques}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {1}, pages = {29--38}, abstract = {

A lot of curve fitting problems of experiment data lead to solution of an overdetermined system of linear equations. But it is not clear prior to that whether the data are exact or contaminated with errors of an unknown nature. Consequently we need to use not only $L_2$-solution of the system but also $L_{\infty}$- or $L_p$-solution.
In this paper, we propose a universal algorithm called the Directional Perturbation Least Squares (DPLS) Algorithm, which can give optimal solutions of an overdetermined system of linear equations in $L_2$, $L_{\infty}$,$L_p (1\leq p＜2)$ norms using only L.S. techniques (in $\S$2). Theoretical principle of the algorithm is given in $\S$ 3. Two examples are given in the end.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9339.html} }
TY - JOUR T1 - Solution of an Overdetermined System of Linear Equations in $L_2$, $L_∞$, $L_P$ Norm Using L.S. Techniques AU - Yang , Shu-Guang AU - Liao , Jian-Wen JO - Journal of Computational Mathematics VL - 1 SP - 29 EP - 38 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9339.html KW - AB -

A lot of curve fitting problems of experiment data lead to solution of an overdetermined system of linear equations. But it is not clear prior to that whether the data are exact or contaminated with errors of an unknown nature. Consequently we need to use not only $L_2$-solution of the system but also $L_{\infty}$- or $L_p$-solution.
In this paper, we propose a universal algorithm called the Directional Perturbation Least Squares (DPLS) Algorithm, which can give optimal solutions of an overdetermined system of linear equations in $L_2$, $L_{\infty}$,$L_p (1\leq p＜2)$ norms using only L.S. techniques (in $\S$2). Theoretical principle of the algorithm is given in $\S$ 3. Two examples are given in the end.  

Yang , Shu-Guang and Liao , Jian-Wen. (1992). Solution of an Overdetermined System of Linear Equations in $L_2$, $L_∞$, $L_P$ Norm Using L.S. Techniques. Journal of Computational Mathematics. 10 (1). 29-38. doi:
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