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Direct and Converse Theorems for Generalized Bernstein-Type Operators

Finta, Zoltán (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.We establish direct and converse theorems for generalized parameter dependent Bernstein-type operators. The direct estimate is given using a K-functional and the inverse result is a strong converse inequality of type A, in the terminology of [2].

Discrete smoothing splines and digital filtration. Theory and applications

Jiří Hřebíček, František Šik, Vítězslav Veselý (1990)

Aplikace matematiky

Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector r = ( r 0 , . . . , r n - 1 ) T with respect to the operations 𝒜 , and to the smoothing parameter α . The resulting function is denoted by σ α ( t ) . The measured sample r is defined on an equally spaced mesh Δ = { t i = i h } i = 0 n - 1 ...

Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

Kamaljit Chowdhary, Paul Dupuis (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...

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