Search results for "approksimointi"
showing 10 items of 38 documents
Convergence of dynamic programming principles for the $p$-Laplacian
2018
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.
On superconvergence techniques
1984
Approximation of pre-twisted Achilles sub-tendons with continuum beam elements
2022
Achilles sub-tendons are materially and geometrically challenging structures that can nearly undergo around 15% elongation from their pre-twisted initial states during physical activities. Sub-tendons' cross-sectional shapes are subject-specific, varying from simple to complicated. Therefore, the Achilles sub-tendons are often described by three-dimensional elements that lead to a remarkable number of degrees of freedom. On the other hand, the continuum-based beam elements in the framework of the absolute nodal coordinate formulation have already been shown to be a reliable and efficient replacement for the three-dimensional continuum elements in some special problems. So far, that element …
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.
Rothin lause
2012
Tämän pro gradu -tutkielman tarkoituksena on esitellä Diofantoksen approksimoinnin tuloksia ja antaa todistus Rothin lauseelle. Diofantoksen approksimoinnissa ollaan kiinnostuneita siitä, kuinka hyvin irrationaalilukuja voidaan arvioida rationaaliluvuilla. Näiden rationaalilukuarvioiden määrän perusteella voidaan antaa riittävä ja välttävä ehto luvun irrationaalisuudesta. Osoittautuu, että ainoastaan irrationaaliluvuilla on ääretön määrä ''hyviä'' arvioita. Tämän ehdon riittävyys ja välttävyys todistetaan ja lisäksi esitellään tehokas menetelmä näiden arvioiden laskemiseksi ketjumurtolukujen avulla. Kun on todettu, että näitä hyviä arvioita on olemassa ja niitä voidaan laskea, voidaan kysyä…
Recovering a variable exponent
2021
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.
Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems
2016
In this thesis, an approximate method introduced to solve time-dependent many-body problems known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations, are introduced. In practice, the associated integral kernels known as the electron Σ and phonon self-energies need to be approximated. The conserving approximations known as the Hartree (-Fock) and the first and second Born approximations, which respect the continuity equation between the electron density and curren…
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
2020
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…
Quantitative Approximation Properties for the Fractional Heat Equation
2017
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…