相关论文: Kozlov-Maz'ya iteration as a form of Landweber ite…

This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…

We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to…

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…

We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…

This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with…

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…

In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is investigated. We show that the proposed method is a convergent…

We prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary,…

In a recent paper, Darvas-Rubinstein proved a convergence result for the Kahler-Ricci iteration, which is a sequence of recursively defined complex Monge-Ampere equations. We introduce the Monge-Ampere iteration to be an analogous, but more…

We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on…

This paper introduces a fast and robust iterative scheme for the elliptic Monge-Amp\`ere equation with Dirichlet boundary conditions. The Monge-Amp\`ere equation is a nonlinear and degenerate equation, with applications in optimal…

We consider a conformally invariant version of the Calder\'on problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main…

We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties…

Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term. The results on existence, uniqueness and asymptotic…

Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational…

Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…

We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned nonlinear conjugate…

We investigate the regularity in $L^p$ ($p>2$) of the gradient of any weak solution of a Cauchy problem with mixed Neumann-power type boundary conditions. Under suitable assumptions we prove the existence of weak solutions that satisfy…

We study the quantitative unique continuation on the boundary for solutions of elliptic equations with Neumann boundary conditions for bounded potentials and boundary potentials on compact manifolds with boundary. The boundary doubling…

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…