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

G. Sonnevend

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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 adaptation of the $k$ -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

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We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse $E$ is viewed as a Mahalanobis circle with center $S$ , radius $r$ , and some positive definite matrix $Σ$ . A very efficient method for solving this problem is proposed. The method uses a modification of the $k$ -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers...

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...

Routh-type $L_{2}$ model reduction revisited

Wiesław Krajewski, Umberto Viaro (2018)

Kybernetika

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A computationally simple method for generating reduced-order models that minimise the $L_{2}$ norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the $L_{2}$ -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques...

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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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 ${[0, 1]}^{2}$ .”