Results 211 to 220 of about 27,741 (236)

On best simultaneous approximations

Russian Mathematical Surveys, 1996
Let \(\alpha= (\alpha_1, \dots \alpha_s) \in\mathbb{R}^s\). An integer point \(\zeta= (p, a_1, \dots, a_s)\in \mathbb{Z}^{s+1}\) is said to be the best simultaneous approximation to \(\alpha \) if \[ D(\zeta)= \max_{1\leq j\leq s} | p\alpha_j- a_j| \cdots\), and then set \[ M_\nu[\alpha] =\left(\begin{matrix} p^{(\nu)} & a_1^{(\nu)} & \dots & a_s^{(\nu)
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On Best Simultaneous Approximation in Normed Linear Spaces

Canadian Mathematical Bulletin, 1974
Let S be a non-empty family of real valued continuous functions on [a, b]. Diaz and McLaughlin [1], [2], and Dunham [3] have considered the problem of simultaneously approximating two continuous functions f1 and f2 by elements of S. If || • || denotes the supremum norm, then the problem is to find an element * ∈ S if it exists, for ...
Goel, D. S., Holland, A. S. B., Nasim, C., Sahney, B. N.   +3 more
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Computation of Best Simultaneous Approximations with a Singularity

Numerical Functional Analysis and Optimization, 1980
ABSTRACT Simultaneous approximation errors are generally discontinuous when the function to be approximated contains a zero in its domain of definition. In this article we indicate how the presence of such a zero (or, equivalently, the resulting singularity in the error expression) affects the computational schemata for finding all the best ...
Irene Grimard, Alexis Bacopoulos
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Best simultaneous approximation in fuzzy normed spaces

2010
Summary: The main purpose of this paper is to consider the t-best simultaneous approximation in fuzzy normed spaces. We develop the theory of t-best simultaneous approximation in quotient spaces. Then, we discuss the relationship in t-proximinality and t-Chebyshevity of a given space and its quotient space.
Goudarzi, Mozafar, Vaezpour, S. Mansour
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Best Simultaneous Approximation

1984
Publisher Summary This chapter considers (F, e· e) as a nontrivial nonarchimedean valued division ring and (E, ee· ee) is a nonzero nonarchimedean normed space over (F, e· e). The chapter discusses a problem that in the nonarchimedean case has a very simple solution: when M ≠ {O}, there is no uniqueness.
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A characterization of an element of best simultaneous approximation

Numerical Functional Analysis and Optimization, 1983
Deutsch [4] has suggested that some problems of best simultaneous approximation might profitably be viewed as problems of best approximation in an appropriate product space. A few authors have touched upon this approach; none, however, have pursued it consistently or developed a complete problem along such a line, even in the simplest of cases. In this
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On the Best Simultaneous Approximation of Functions in the Bergman Space B2

Russian Mathematics, 2023
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Best Simultaneous Approximation in Quotient Spaces

2016
We discuss the problem of best simultaneous approximation in quotient spaces when the underlying spaces are metric linear spaces. We characterize simultaneous proximinality, simultaneous Chebyshevity, simultaneous pseudo-Chebyshevity and simultaneous quasi-Chebyshevity and see how these are transmitted to and from quotient spaces. The results proved in
T. D. Narang, Sahil Gupta
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Best Simultaneous Approximation (Chebyshev Centers)

1984
The problem of approximating simultaneously a set of data in a given metric space by a single element of an approximating family arises naturally in many practical problems. A common procedure is to choose the “best” approximant by a least squares principle, which has the advantages of existence, uniqueness, stability and easy computability.
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A Note on Best Simultaneous Approximation in Normed Linear Spaces

Canadian Mathematical Bulletin, 1976
The purpose of the present note is to point out that the results of D. S. Goel, A. S. B. Holland, C. Nasim and B. N. Sahney [1] on best simultaneous approximation are easy consequences of simple facts about convex functions. Given a normed linear space X, a convex subset K of X, and points x1, x2 in X, [1] discusses existence and uniqueness of K* ∈ K ...
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