Search results for "Convergence"

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.

Thermal deformations of inhomogeneous elastic plates

1995

We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear was well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Karman equations are formulated. Its is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Karman equations

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.

Asymptotical Convergence Evaluation for a Parabolic Problem Arising in Circuit Theory

1990

Plate-tectonic processes at ca. 2.0 Ga: Evidence from >600 km of plate convergence

2019

Abstract We addressed when plate-tectonic processes first started on Earth by examining the ca. 2.0 Ga Limpopo orogenic belt in southern Africa. We show through palinspastic reconstruction that the Limpopo orogen originated from >600 km of west-directed thrusting, and the thrust sheet was subsequently folded by north-south compression. The common 2.7–2.6 Ga felsic plutons in the Limpopo thrust sheet and the absence of an arc immediately predating the 2.0 Ga Limpopo thrusting require the Limpopo belt to be an intracontinental structure. The similar duration (∼40 m.y.), slip magnitude (>600 km), slip rate (>15 mm/yr), tectonic setting (intracontinental), and widespread an…

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…

Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow

2011

AbstractThe convergence of many iterative procedures, in particular that of the conjugate gradient method, strongly depends on the condition number of the linear system to be solved. In cases with a large condition number, therefore, preconditioning is often used to transform the system into an equivalent one, with a smaller condition number and therefore faster convergence. For Poisson-like difference equations with flat grids, the vertical part of the difference operator is dominant and tridiagonal and can be used for preconditioning. Such a procedure has been applied to incompressible atmospheric flows to preserve incompressibility, where a system of Poisson-like difference equations is …

Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using cholesky dec…

2004

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model using Cholesky decomposition of the two-electron integrals is presented. Significantly reducing storage demands and computational effort without sacrificing accuracy compared to the conventional model, the algorithm is well suited for large-scale applications. Extensive basis set convergence studies are presented for the static and frequency-dependent electric dipole polarizability of benzene and C60, and for the optical rotation of CNOFH2 and (−)-trans-cyclooctene (TCO). The origin-dependence of the optical rotation is calculated and shown to persist for CC2 even at basis set convergence. …