Best Simultaneous Approximation of Finite Set in Inner Product Space
Affiliation(s)
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
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.
Cite this paper
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.
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.
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.
[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.