Best Simultaneous Approximation of Finite Set in Inner Product Space

DOI: 10.4236/apm.2013.35069   PDF   HTML   XML   3,252 Downloads   5,274 Views  

Abstract

In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we define best approximation of each point and achieve our purpose.

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S. Akbarzadeh and M. Iranmanesh, "Best Simultaneous Approximation of Finite Set in Inner Product Space," Advances in Pure Mathematics, Vol. 3 No. 5, 2013, pp. 479-481. doi: 10.4236/apm.2013.35069.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] F.Deutsch, “Best Approximation in Inner Product Spaces,”Springer, Berlin, 2001.
[2] D.Fang,X.Luo and Chong Li, “Nonlinear Simultaneous Approximation in Complete Lattice Banach Spaces,”Taiwanese Journal of Mathematics, 2008.
[3] W. C. Charles, “Linear Algebra,” 1968, p. 62.
[4] V. Prasolov and V. M. Tikhomirov, “Geometry,” American Mathematical Society, 2001, p. 22.

  
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