• Title, Summary, Keyword: best approximation

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Strongly Unique Best Coapproximation

  • RAO, GEETHA S.;SARAVANAN, R.
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.519-538
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    • 2003
  • This paper delineates some fundamental properties of the set of strongly unique best coapproximation. Uniqueness of strongly unique best coapproximation is studied. Some characterizations of strongly unique best coapproximation and strongly unique best approximation are obtained. Some more results concerning strongly unique best uniform coapproximation and strongly unique best uniform approximation are presented. Some relations between best uniform approximation and strongly unique best uniform coapproximation are established.

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GEOMETRIC CONIC SPLINE APPROXIMATION IN CAGD

  • Ahn, Young-Joon
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.331-347
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    • 2002
  • We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

SOME ALGORITHMS OF THE BEST SIMULTANEOUS APPROXIMATION

  • Rhee, Hyang J.
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.141-148
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    • 2009
  • We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of $\mathbb{R}^{m}$ satisfying $X=\overline{intX}$, S is an n-dimensional subspace of C(X), and $\mu$ is any 'admissible' measure on X. For any l-tuple $f_1,\;{\cdots},\;f_{\ell}$ in C(X), we present various ideas for best approximation to F from S(F). The problem of best (both one and two-sided) approximation is a linear programming problem.

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TWO-SIDED BEST SIMULTANEOUS APPROXIMATION

  • Rhee, Hyang Joo
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.4
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    • pp.705-710
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    • 2010
  • Let $C_1(X)$ be a normed linear space over ${\mathbb{R}}^m$, and S be an n-dimensional subspace of $C_1(X)$ with spaned by {$s_1,{\cdots},s_n$}. For each ${\ell}$- tuple vectors F in $C_1(X)$, the two-sided best simultaneous approximation problem is $$\min_{s{\in}S}\;\max\limits_{i=1}^\ell\{{\parallel}f_i-s{\parallel}_1\}$$. A $s{\in}S$ attaining the above minimum is called a two-sided best simultaneous approximation or a Chebyshev center for $F=\{f_1,{\cdots},f_{\ell}\}$ from S. This paper is concerned with algorithm for calculating two-sided best simultaneous approximation, in the case of continuous functions.

One-sided best simultaneous $L_1$-approximation for a compact set

  • Park, Sung-Ho;Rhee, Hyang-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.127-140
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    • 1998
  • In this paper, we discuss the characterizations and uniqueness of a one-sided best simultaneous approximation for a compact subset from a convex subset of a finite-dimensional subspace of a normed linear space $C_1(X)$. The motivation is furnished by the characterizations of the one-sided best simultaneous approximations for a finite subset ${f_1, \ldots, f_\ell}$ for any $\ell \in N$.

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BEST PARAMETRIC APPROXIMATION IN $C_1$(X)

  • Rhee, Hyang-Joo
    • The Pure and Applied Mathematics
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    • v.8 no.1
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    • pp.9-14
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    • 2001
  • In some problems of abstract approximation theory the approximating set depends on some parameter p. In this paper, we make a set M(f) depends on the element f, $\phi$ and then best approximations are sought from a subset M(f) of M.

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Best Approximation Result in Locally Convex Space

  • Nashine, Hemant Kumar
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.389-397
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    • 2006
  • A fixed point theorem of Singh and Singh [10] is generalized to locally convex spaces and the new result is applied to extend a result on invariant approximation of Jungck and Sessa [5].

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COMMON FIXED POINT THEOREM FOR OCCASIONALLY WEAKLY BAISED MAPPINGS AND ITS APPLICATION TO BEST APPROXIMATION

  • Deshpande, Bhavana;Chouhan, Suresh
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.543-552
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    • 2012
  • The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].