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On the optimization of initial conditions for a model parameter estimation

Matonoha, Ctirad, Papáček, Štěpán, Kindermann, Stefan (2017)

Programs and Algorithms of Numerical Mathematics

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...

On the randomized complexity of Banach space valued integration

Stefan Heinrich, Aicke Hinrichs (2014)

Studia Mathematica

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by c n - r / d - 1 + 1 / p if and only if X is of equal norm type p.

Operators approximating partial derivatives at vertices of triangulations by averaging

Josef Dalík (2010)

Mathematica Bohemica

Let 𝒯 h be a triangulation of a bounded polygonal domain Ω ⊂ ℜ 2 , ℒ h the space of the functions from C ( Ω ¯ ) linear on the triangles from 𝒯 h and Π h the interpolation operator from C ( Ω ¯ ) to ℒ h . For a unit vector z and an inner vertex a of 𝒯 h , we describe the set of vectors of coefficients such that the related linear combinations of the constant derivatives ∂ Π h ( u ) / ∂ z on the triangles surrounding a are equal to ∂ u / ∂ z ( a ) for all polynomials u of the total degree less than or equal to two. Then we prove that, generally, the values of the...

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