Rational Functions with Partial Quotients of Small Degree in Their Continued Fraction Expansion.
Rational interpolation: analytical solution.
Rational Krylov for nonlinear eigenproblems, an iterative projection method
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably...
Rationale Interpolation, Normalität und Monosplines.
Rationale Tschebyscheff-Approximation über unbeschränkten Intervallen.
Real and complex pseudozero sets for polynomials with applications
Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...
Realistic Error Bounds for a Simple Eigenvalue and its Associated Eigenvector.
Realization of Dirichlet conditions in RKPM
Realization of the dynamics of ODE's in scalar parabolic PDE's
Rearrangement of lattice particles.
Recent developments in the theory of function spaces with dominating mixed smoothness
The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...
Recent developments in wavelet methods for the solution of PDE's
After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.
Recent progress in the integration of Poisson systems via the mid-point rule and Runge-Kutta algorithm.
Recent results in the approximation of free boundaries
Recherche de partitions hiérarchisées optimales (-structure de hiérarchies optimales)
Reconstruction algorithms for an inverse medium problem
In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability...
Reconstruction of map projection, its inverse and re-projection
This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections...
Reconstruction of quadratic curves in 3-D from two or more perspective views.
Reconstruction of the right-hand side of the elliptical equation from observation data obtained at the boundary
Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions
We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material properties of the coating and they have been obtained in the previous work [B. Aslanyürek, H. Haddar and H.Şahintürk, Wave Motion 48 (2011) 681–700]...