Convergence Rate Research Papers - Academia.edu (original) (raw)

We prove the existence and uniqueness of a strong solution for a parabolic singular equation in which we combine Dirichlet with integral boundary conditions given only on parts of the boundary. The proof uses a priori estimate and the... more

We prove the existence and uniqueness of a strong solution for a parabolic singular equation in which we combine Dirichlet with integral boundary conditions given only on parts of the boundary. The proof uses a priori estimate and the density of the range of the operator generated by the problem considered.

1.1. Families of Graphs. In this paper we investigate the distribution of the second largest eigenvalue associated to d-regular undirected graphs1. A graph G is bipartite if the vertex set of G can be split into two disjoint sets A and B... more

1.1. Families of Graphs. In this paper we investigate the distribution of the second largest eigenvalue associated to d-regular undirected graphs1. A graph G is bipartite if the vertex set of G can be split into two disjoint sets A and B such that every edge connects a vertex in A with one in B, and G is d-regular if every vertex is connected to exactly d vertices. To any graph G we may associate a real symmetric matrix, called its adjacency matrix, by setting aij to be the number of edges connecting vertices i and j. Let us write the eigenvalues of G by λ1(G) ≥···≥ λN (G), where G has N ...

The development of scalable robust solvers for unstructured finite element applications related to viscous flow problems in earth sciences is an active research area. Solving high‐resolution convection problems with order of magnitude 108... more

The development of scalable robust solvers for unstructured finite element applications related to viscous flow problems in earth sciences is an active research area. Solving high‐resolution convection problems with order of magnitude 108 degrees of freedom requires solvers that scale well, with respect to both the number of degrees of freedom as well as having optimal parallel scaling characteristics on computer clusters. We investigate the use of a smoothed aggregation (SA) algebraic multigrid (AMG)‐type solution strategy to construct efficient preconditioners for the Stokes equation. We integrate AMG in our solver scheme as a preconditioner to the conjugate gradient method (CG) used during the construction of a block triangular preconditioner (BTR) to the Stokes equation, accelerating the convergence rate of the generalized conjugate residual method (GCR). We abbreviate this procedure as BTA‐GCR. For our experiments, we use unstructured grids with quadratic finite elements, makin...

This paper is concerned,with the development,of adaptive,wavelet methods,for the hardening problem,in elastoplasticity. Wepropose,a Rothe method,using some implicit scheme in time. Then, we consider a standard elastic predictor–plastic... more

This paper is concerned,with the development,of adaptive,wavelet methods,for the hardening problem,in elastoplasticity. Wepropose,a Rothe method,using some implicit scheme in time. Then, we consider a standard elastic predictor–plastic corrector method.

We deal with locally ill-posed nonlinear operator equations F (x) = y in L2(0, 1), where the Fréchet derivatives A = F '(x0) of the nonlinear forward operator F are compact linear integral operators A = M ◦ J with a multiplication... more

We deal with locally ill-posed nonlinear operator equations F (x) = y in L2(0, 1), where the Fréchet derivatives A = F '(x0) of the nonlinear forward operator F are compact linear integral operators A = M ◦ J with a multiplication operator M with integrable multiplier function m and with the simple integration operator J. In particular, we give examples of nonlinear inverse problems in natural sciences and stochastic finance that can be written in such a form with linearizations that contain multiplication operators. Moreover, we consider the corresponding ill-posed linear operator equations Ax = y and their degree of ill-posedness. In particular, we discuss the fact that the noncompact multiplication operator M has only a restricted influence on this degree of ill-posedness even if m has essential zeros of various order.

In this paper, we are going to improve the enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces presented by Neubauer in (14). The new message is that rates are shown to be independent of... more

In this paper, we are going to improve the enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces presented by Neubauer in (14). The new message is that rates are shown to be independent of the residual norm exponents 1 p < 1 in the functional to be minimized for obtaining regularized solutions. However, on the one hand the smoothness of the image space influences the rates, and on the other hand best possible rates require specific choices of the regularization parameters > 0. In the limiting case p = 1, the -values must not tend to zero as the noise level decreases, but has to converge to a fixed positive value characterized by properties of the solution.

The estimation of a quantile density function in the biased nonparametric regression model is investigated. We propose and develop a new waveletbased methodology for this problem. In particular, an adaptive hard thresholding wavelet... more

The estimation of a quantile density function in the biased nonparametric regression model is investigated. We propose and develop a new waveletbased methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The performance of the proposed estimator is investigated by a numerical study.

In this paper, new algorithm is proposed for fictitious mass of Dynamic Relaxation (DR) method with viscous damping. First, the incremental equations are derived for DR procedure. By using the transformed Gershgörin theory, new boundaries... more

In this paper, new algorithm is proposed for fictitious mass of Dynamic Relaxation (DR) method with viscous damping. First, the incremental equations are derived for DR procedure. By using the transformed Gershgörin theory, new boundaries are achieved for fictitious mass. This formulation leads to a new algorithm for viscous DR method. For evaluating the efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed by elastic linear and geometrically nonlinear behaviors. Results show that the proposed scheme for fictitious mass improves the convergence rate of DR method so that the suggested algorithm presents the structural response with less iteration in comparison with other common DR techniques.