An optimal sequential algorithm for the uniform approximation of convex functions on $[0,1]^2$.

G. Sonnevend

Displaying similar documents to “An optimal sequential algorithm for the uniform approximation of convex functions on ${[0, 1]}^{2}$ .”

A descent algorithm for $ε$ - approximation of continuous functions with values in unitary space

M. Janc (1982)

Matematički Vesnik

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On the weighted Euclidean matching problem in $ℝ^{d}$

Birgit Anthes, Ludger Rüschendorf (2001)

Applicationes Mathematicae

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A partitioning algorithm for the Euclidean matching problem in $ℝ^{d}$ is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time $n {(l o g n)}^{p - 1}$ and approximates the optimal matching in the probabilistic sense.

The general methods of finding the sum $S_{n}$ for all kinds of series

K. Orlov (1981)

Matematički Vesnik

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Uniform convergence of the greedy algorithm with respect to the Walsh system

Martin Grigoryan (2010)

Studia Mathematica

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For any 0 < ϵ < 1, p ≥ 1 and each function $f \in L^{p} [0, 1]$ one can find a function $g \in L^{\infty} [0, 1)$ with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence $| c_{k} (g) | : k \in s p e c (g)$ is decreasing, where $c_{k} (g)$ is the sequence of Fourier coefficients of g with respect to the Walsh system.

On FU( $p$ )-spaces and $p$ -sequential spaces

Salvador García-Ferreira (1991)

Commentationes Mathematicae Universitatis Carolinae

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Following Kombarov we say that $X$ is $p$ -sequential, for $p \in α^{*}$ , if for every non-closed subset $A$ of $X$ there is $f \in^{α} X$ such that $f (α) \subseteq A$ and $\bar{f} (p) \in X ∖ A$ . This suggests the following definition due to Comfort and Savchenko, independently: $X$ is a FU( $p$ )-space if for every $A \subseteq X$ and every $x \in A^{-}$ there is a function $f \in^{α} A$ such that $\bar{f} (p) = x$ . It is not hard to see that $p \leq_{RK} q$ ( $\leq_{RK}$ denotes the Rudin–Keisler order) $\Leftrightarrow$ every $p$ -sequential space is $q$ -sequential $\Leftrightarrow$ every FU( $p$ )-space is a FU( $q$ )-space. We generalize the spaces $S_{n}$ to construct examples of...

A Natural Class of Sequential Banach Spaces

Jarno Talponen (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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We introduce and study a natural class of variable exponent $ℓ^{p}$ spaces, which generalizes the classical spaces $ℓ^{p}$ and c₀. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

Stanisław Kwapień, Jan Mycielski (2001)

Studia Mathematica

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The Kaczmarz algorithm of successive projections suggests the following concept. A sequence $(e_{k})$ of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and $x ₙ = x_{n - 1} + α ₙ e ₙ$ , where $α ₙ = ⟨ x - x_{n - 1}, e ₙ ⟩$ . We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.

The polynomial approximation of continuous functions defined on $(- \infty, \infty)$

Leetsch C. Hsu (1959)

Czechoslovak Mathematical Journal

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An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan

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The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$ - $s$ transformation and $Q R$ -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

Banach Center Publications

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We present an estimation of the $H_{k ₀, k_{r}}^{q, α} f$ and $H_{λ, u}^{ϕ, α} f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

$L_{\infty}$ -Convergence of Finite Element Approximation

J. A. Nitsche (1975)

Publications mathématiques et informatique de Rennes

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Displaying similar documents to “An optimal sequential algorithm for the uniform approximation of convex functions on [ 0 , 1 ] 2 .”

Displaying similar documents to “An optimal sequential algorithm for the uniform approximation of convex functions on ${[0, 1]}^{2}$ .”