International portfolios: A comparison of solution methods
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This survey focuses on a class of methods for image alignment based on a global, iterative optimization. We synthetically describe the existing methods (included the recent Efficient Second Order Method), compare their theoretical aspects, computational co ...
The need for optimal control of processes under a restricted amount of resources renders first order optimization methods a viable option. Although computationally cheap, these methods typically suffer from slow convergence rates. In this work we discuss t ...
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to mult ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standar ...
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the non-linear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows one to include magnetostrictive effects into the simul ...
This article shows that portfolio constraints can give rise to rational asset pricing bubbles in equilibrium even if there are unconstrained agents in the economy who can benefit from the induced limited arbitrage opportunities. Furthermore, it is shown th ...
We introduce a new family of explicit integrators for stiff Ito stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from th ...
