Search results for "convergence"
showing 10 items of 655 documents
Klum@Gtap: Introducing Biophysical Aspects of Land-Use Decisions into a General Equilibrium Model: a Coupling Experiment
2006
In this paper the global agricultural land use model KLUM is coupled to an extended version of the computable general equilibrium model (CGE) GTAP in order to consistently assess the integrated impacts of climate change on global cropland allocation and its implication for economic development. The methodology is innovative as it introduces dynamic economic land-use decisions based also on the biophysical aspects of land into a state-of-the-art CGE; it further allows the projection of resulting changes in cropland patterns on a spatially more explicit level. A convergence test and illustrative future simulations underpin the robustness and potentials of the coupled system. Reference simulat…
KLUM@GTAP: Introducing Biophysical Aspects of Land-Use Decisions into a Computable General Equilibrium Model a Coupling Experiment
2008
In this paper, the global agricultural land use model Kleines Land Use Model is coupled to an extended version of the computable general equilibrium model (CGE) Global Trade Analysis Project in order to consistently assess the integrated impacts of climate change on global cropland allocation and its implication for economic development. The methodology is innovative as it introduces dynamic economic land-use decisions based also on the biophysical aspects of land into a state-of-the-art CGE; it further allows the projection of resulting changes in cropland patterns on a spatially more explicit level. A convergence test and illustrative future simulations underpin the robustness and potenti…
Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques
2008
Abstract This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, i…
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
2013
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
𝒦-convergence as a new tool in numerical analysis
2019
Abstract We adapt the concept of $\mathscr{K}$-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.
Third-order iterative methods without using any Fréchet derivative
2003
AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.
Global convergence and rate of convergence of a method of centers
1994
We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems.
The rate of multiplicity of the roots of nonlinear equations and its application to iterative methods
2015
Nonsimple roots of nonlinear equations present some challenges for classic iterative methods, such as instability or slow, if any, convergence. As a consequence, they require a greater computational cost, depending on the knowledge of the order of multiplicity of the roots. In this paper, we introduce dimensionless function, called rate of multiplicity, which estimates the order of multiplicity of the roots, as a dynamic global concept, in order to accelerate iterative processes. This rate works not only with integer but also fractional order of multiplicity and even with poles (negative order of multiplicity).
On finite element approximation of the gradient for solution of Poisson equation
1981
A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
Iterative approximation to a coincidence point of two mappings
2015
In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.