All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 43 Next

Displaying 841 – 860 of 9149

Showing per page

A priori error estimates for finite element discretizations of a shape optimization problem

Bernhard Kiniger, Boris Vexler (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples.

A priori error estimates for Lagrange interpolation on triangles

Kenta Kobayashi, Takuya Tsuchiya (2015)

Applications of Mathematics

We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation....

A priori error estimates for reduced order models in finance

Ekkehard W. Sachs, Matthias Schu (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...

A proof of monotony of the Temple quotients in eigenvalue problems

Karel Rektorys (1984)

Aplikace matematiky

If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue λ 1 , the sequences of the so-called Schwarz quatients (which are upper bounds for λ 1 ) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...

A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

Douglas Bunker, Lixing Han, Shu Hua Zhang (2013)

Applications of Mathematics

The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions....

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

Pang, Li-Ping, Xia, Zun-Quan (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an...

A Q -scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shadow water system

Manuel Castro, Jorge Macías, Carlos Parés (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The goal of this paper is to construct a first-order upwind scheme for solving the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids. This is done by generalizing a numerical scheme presented by Bermúdez and Vázquez-Cendón [3, 26, 27] for solving one-layer shallow water equations, consisting in a Q -scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...

A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system

Manuel Castro, Jorge Macías, Carlos Parés (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The goal of this paper is to construct a first-order upwind scheme for solving the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids. This is done by generalizing a numerical scheme presented by Bermúdez and Vázquez-Cendón [3, 6, 27] for solving one-layer shallow water equations, consisting in a Q-scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...

Currently displaying 841 – 860 of 9149