We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a reference solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upo...

Proving the existence of a solution to a system of real equations is a central issue in numerical analysis. In many situations, the system of equations depend on parameters which are not exactly known. It is then natural to aim proving the existence of a solution for all values of these parameters in some given domains. This is the aim of the parametrization of existence tests. A new parametric...

The minimum error entropy (MEE) criterion is an important learning criterion in information theoretical learning (ITL). However, the MEE solution cannot be obtained in closed form even for a simple linear regression problem, and one has to search it, usually, in an iterative manner. The fixed-point iteration is an efficient way to solve the MEE solution. In this work, we study a fixed-point MEE...

The aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems. We propose a new approach generalizing the standard speed method, which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional. The resulting approach c...

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured (and therefore noisy) fa...

We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of near-independence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive fr...

We investigate the convergence of the self-consistent field (SCF) iteration used to solve a class of nonlinear eigenvalue problems. We show that for the class of problem considered, the SCF iteration produces a sequence of approximate solutions that contain two convergent subsequences. These subsequences may converge to two different limit points, neither of which is the solution to the nonline...

Necessary and sufficient conditions for the convergence of Picard iteration to a fixed point for a continuous mapping in metric spaces are established. As application, we prove the convergence theorem of Ishikawa iteration to a fixed point for a nonexpansive mapping in Banach spaces. 2004 Elsevier Inc. All rights reserved.

The purpose of this paper is to investigate fixed point arithmetic in ring-based Somewhat Homomorphic Encryption (SHE) schemes. We provide three main contributions: Firstly, we investigate the representation of fixed point numbers. We analyse the two representations from Dowlin et al, representing a fixed point number as a large integer (encoded as a scaled polynomial) versus a polynomial-based...