Search results for " convergence."
showing 10 items of 251 documents
Quantitative approximation of certain stochastic integrals
2002
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.
Superconvergence phenomenon in the finite element method arising from averaging gradients
1984
We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.
VARIANTS OF A SELECTION PRINCIPLE FOR SEQUENCES OF REGULATED AND NON-REGULATED FUNCTIONS
2008
Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all functions mapping $T$ into $X$. Given $\vep>0$ and $f\in X^T$, we denote by $N(\vep,f,T)$ the least upper bound of those $n\in\NB$, for which there exist numbers $s_1,\dots,s_n,t_1,\dots,t_n$ from $T$ such that $s_1\vep$ for all $i=1,\dots,n$ ($N(\vep,f,T)=0$ if there are no such $n$'s). The following pointwise selection principle is proved: {\em If a sequence of functions\/ $\{f_j\}_{j=1}^\infty\subset X^T$ is such that the closure in $X$ of the sequence\/ $\{f_j(t)\}_{j=1}^\infty$ is compact for each $t\in T$ and\/ $\limsup_{j\to\infty}N(\vep,f_j,T)0$, then\/ $\{f_j\}_{j=1}^\infty$ contains …
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
A pointwise selection principle for metric semigroup valued functions
2008
Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…
The Magnus expansion and some of its applications
2008
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…
A predictive function optimization algorithm for multi-spectral skin lesion assessment
2015
The newly introduced Kubelka-Munk Genetic Algorithm (KMGA) is a promising technique used in the assessment of skin lesions. Unfortunately, this method is computationally expensive due to its function inverting process. In the work of this paper, we design a Predictive Function Optimization Algorithm in order to improve the efficiency of KMGA by speeding up its convergence rate. Using this approach, a High-Convergence-Rate KMGA (HCR-KMGA) is implemented onto multi-core processors and FPGA devices respectively. Furthermore, the implementations are optimized using parallel computing techniques. Intensive experiments demonstrate that HCR-KMGA can effectively accelerate KMGA method, while improv…
groups acting on the line and the circle with at most N fixed points
2022
A classical theme in dynamical systems is that the first fundamental information comes from the understanding of periodic orbits. When studying group actions, this means that we want to understand the fixed points of elements of the group, and a natural question that emerges from that is: Which groups of homeomorphisms can act on a 1-manifold having all non-trivial elements with at most N fixed points? Our main objective in this work is to approach that question and understand what properties can such dynamical hypothesis induces to the group.For the case N=0, a classical result from O. Hölder implies that such group of homeomorphisms acting on the line is always semi-conjugate to a subgrou…
Do distantly related parasites rely on the same proximate factors to alter the behaviour of their hosts?
2006
Phylogenetically unrelated parasites often increase the chances of their transmission by inducing similar phenotypic changes in their hosts. However, it is not known whether these convergent strategies rely on the same biochemical precursors. In this paper, we explored such aspects by studying two gammarid species ( Gammarus insensibilis and Gammarus pulex ; Crustacea: Amphipoda: Gammaridae) serving as intermediate hosts in the life cycle of two distantly related parasites: the trematode, Microphallus papillorobustus and the acanthocephalan, Polymorphus minutus . Both these parasite species are known to manipulate the behaviour of their amphipod hosts, bringing them towards the water surfa…
About the finite convergence of the proximal point algorithm
1988
We study the finite convergence property of the proximal point algorithm applied to the partial inverse, with respect to a subspace, of the subdifferential of a polyhedral convex function. Using examples we show how sufficient conditions providing the finite convergence can be realized and we give a case with non finite termination.