Related papers: A refined invariant subspace method and applicatio…
Unsupervised domain adaptation (UDA) aims to transfer and adapt knowledge from a labeled source domain to an unlabeled target domain. Traditionally, subspace-based methods form an important class of solutions to this problem. Despite their…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…
A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
The main purpose of this paper is to improve our transposition method to solve both vector-valued and operator-valued backward stochastic evolution equations with a general filtration. As its application, we obtain a general Pontryagin-type…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We introduce and investigate in this paper a new convenient method of introduction of a norm in the multidimensional rearrangement probability invariant space.
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…