Search results for " Computational"
showing 10 items of 661 documents
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
The Abelian Kernel of an Inverse Semigroup
2020
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…
Computational aspects in checking of coherence and propagation of conditional probability bounds
2000
In this paper we consider the problem of reducing the computational difficulties in g-coherence checking and propagation of imprecise conditional probability assessments. We review some theoretical results related with the linear structure of the random gain in the betting criterion. Then, we propose a modi ed version of two existing algorithms, used for g-coherence checking and propagation, which are based on linear systems with a reduced number of unknowns. The reduction in the number of unknowns is obtained by an iterative algorithm. Finally, to illustrate our procedure we give some applications.
Algorithms for coherence checking and propagation of conditional probability bounds
2001
In this paper, we propose some algorithms for the checking of generalized coherence (g-coherence) and for the extension of imprecise conditional probability assessments. Our concept of g-coherence is a generalization of de Finetti’s coherence principle and is equivalent to the ”avoiding uniform loss” property for lower and upper probabilities (a la Walley). By our algorithms we can check the g-coherence of a given imprecise assessment and we can correct it in order to obtain the associated coherent assessment (in the sense of Walley and Williams). Exploiting some properties of the random gain we show how, in the linear systems involved in our algorithms, we can work with a reduced set of va…
Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
2020
Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind,…
Euclid preparation: XI. Mean redshift determination from galaxy redshift probabilities for cosmic shear tomography
2021
Ilbert, O., et al. (Euclid Collaboration)
Liftings and extensions of operators in Brownian setting
2020
We investigate the operators T on a Hilbert space H which have 2-isometric liftings S with the property S ∗ S H ⊂ H . We show that such liftings are closely related to some extensions of T, which h...
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed