Results 251 to 260 of about 40,876 (272)

Weak Type Inequalities for Best Simultaneous Approximation in Banach Spaces

Journal of Approximation Theory, 1999
For arbitrary Banach spaces Butzer and Scherer in 1968 showed that the approximation order of best approximation can characterized by the order of certain K-functionals.
Jansche, Stefan
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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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Best Approximation Characterizations

1986
The metric projection P A is the set-valued function which carries x ∈ E to its (possibly empty) best approximation set in A ⊂ E., i.e. P A x ≡ {y ∈ A; ǁx - yǁ = d(x,A)}.
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Characterization of Best Approximations

2001
We give a characterization theorem for best approximations from convex sets. This result will prove useful over and over again throughout the book. Indeed, it will be the basis for every characterization theorem that we give. The notion of a dual cone plays an essential role in this characterization.
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The Characterization of Best Nonlinear Tchebycheff Approximations

1959
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Consider a continuous function, F([...]) of n parameters and [...]. Such a function is said to have Property NS if the following theorem is valid for every continuous function, f(x): THEOREM: F([...]) is a best approximation to f(x) if ...
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Characterizations of the strongly unique best approximations

Numerical Functional Analysis and Optimization, 1985
The purpose of this paper is two folded. First, we present some results on strongly Kolmogorov sets, some of which parallel those for Kolmogorov sets. Secondly, we give two conditions which are sufficient for an element of a strongly Kolmogorov set to be a strongly unique best approximation. Then these conditions are shown to be necessary if additional
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Characterization of Generalized Lipschitz Classes by Best Approximation with Splines

SIAM Journal on Numerical Analysis, 1974
Equivalence theorems for best approximation by splines with equidistant nodes on a finite interval are established. They yield characterizations of the generalized Lipschitz spaces $(\omega _r (t,f)_p $ being the rth modulus of continuity) \[ Lip(\psi ,q,r;p) = \{ f \in L_p (a,b):\left\{ {\begin{array}{*{20}c} {\int_0^1 {[\psi ^{ - 1} (t)\omega _r (t,f)
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Characterizing nonconvex constrained best approximation using Robinson’s constraint qualification

Optimization Letters, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hossein Mohebi, Morteza Sheikhsamani
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A GENERAL CHARACTERIZATION OF BEST RESTRICTED RANGE APPROXIMATIONS

Quaestiones Mathematicae, 1997
Abstract A general characterization of best restricted range approximations is established under an arbitrary norm on C [a, b]. Consequently, many previous characterizations of various best constrained approximations can be treated as special cases of this general characterization theorem.
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Characterizations of Best Complex Chebyshev Approximate Solutions of $Av = b$

SIAM Journal on Numerical Analysis, 1976
Let $Av = b$ be an overdetermined system of m complex equations in n unknowns with rank $(A) = k$ and $m \geqq 2k + 1$. It is shown that if $x_\infty $ is a Chebyshev solution of $Av = b$, then $x_\infty $ is also a Chebyshev solution of a $2k + 1 \times n$ subsystem of $Av = b,A_{2k + 1} v = b_{2k + 1} $. Furthermore, $\| {b - Ax_\infty } \|_\infty = \
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