相关论文: Iterative Solution of the Ornstein-Zernike Equatio…
We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first order periodic boundary value problem with…
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…
For an infinite Toeplitz matrix $T$ with nonnegative real entries we find the conditions, under which the equation $\boldsymbol{x}=T\boldsymbol{x}$, where $\boldsymbol{x}$ is an infinite vector-column, has a nontrivial bounded positive…
It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
This work develops extensions of Steffensen's method to provide new tools for solving the semi-blind image reverse filtering problem. Two extensions are presented: a parametric Steffensen's method for accelerating the Mann iteration, and a…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
The nonlinear recombination equation from population genetics has a long history and is notoriously difficult to solve, both in continuous and in discrete time. This is particularly so if one aims at full generality, thus also including…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
Solutions to differential equations, which are used to model physical systems, are computed numerically by solving a set of discretized equations. This set of discretized equations is reduced to a large linear system, whose solution is…