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On the Operational Solution of a System of Fractional Differential Equations

Takači, Dj., Takači, A. (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and...

On the optimal setting of the h p -version of the finite element method

Chleboun, Jan (2013)

Programs and Algorithms of Numerical Mathematics

The goal of this contribution is to find the optimal finite element space for solving a particular boundary value problem in one spatial dimension. In other words, the optimal use of available degrees of freedom is sought after. This is done through optimizing both the mesh and the polynomial degree of the basis functions. The resulting combinatorial optimization problem is solved in parallel by a Matlab program running on a cluster of multi-core personal computers.

On the Optimality of Sample-Based Estimates of the Expectation of the Empirical Minimizer***

Peter L. Bartlett, Shahar Mendelson, Petra Philips (2010)

ESAIM: Probability and Statistics

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates...

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 parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations

Jiří Egermaier, Hana Horníková (2022)

Applications of Mathematics

In this paper, we deal with the optimal choice of the parameter γ for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter γ for various problem parameters (Reynolds number, mesh refinement) and especially for...

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