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On the Arithmetic of Errors

Markov, Svetoslav, Hayes, Nathan (2010)

Serdica Journal of Computing

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of...

On the Asymptotic Analys of a Non-Symmetric Bar

Abderrazzak Majd (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.

On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations

A. I. Fedotov (2002)

Archivum Mathematicum

We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces H s via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when s > 1 / 2 allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.

On the autocorrelation function of a trended series.

Cecilio Mar Molinero (1985)

Qüestiió

Equations are derived for the autocorrelation function of a trended series. The special case of a linear trend is analysed in detail. It is shown that the zero of the autocorrelation function of a trended series is, in general, only dependent on the length of the series. This result is valid for stochastic and deterministic trends.

On the best choice of a damping sequence in iterative optimization methods.

Leonid N. Vaserstein (1988)

Publicacions Matemàtiques

Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.

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