相关论文: Developing an Analytical Fixed Source Solver for t…

The general solution of the one-dimensional stationary Schroedinger equation in the form of a formal power series is considered. Its efficiency for numerical analysis of initial value and boundary value problems is discussed.

We introduce numerical solvers for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. Due to the quadratic collision operator in the Boltzmann equation, the SGS method requires solving a nonlinear system…

In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed…

The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…

A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…

We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…

he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…

We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…

In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…

Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…

In this paper, we propose a new general and stable fixed-point approach to compute the resolvents of the composition of a set-valued maximal monotone operator with a linear bounded mapping. Weak, strong and linear convergence of the…

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described.…

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix $A$. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to…

In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor…