Related papers: Dynamical Systems Method for solving ill-condition…
Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems.…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…
We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
Solving motion tasks autonomously and accurately is a core ability for intelligent real-world systems. To achieve genuine autonomy across multiple systems and tasks, key challenges include coping with unknown dynamics and overcoming the…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote…
In recent years, the Deep Learning Alternating Minimization (DLAM), which is actually the alternating minimization applied to the penalty form of the deep neutral networks training, has been developed as an alternative algorithm to overcome…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
Simultaneous Localization and Mapping (SLAM) stands as one of the critical challenges in robot navigation. A SLAM system often consists of a front-end component for motion estimation and a back-end system for eliminating estimation drifts.…
Large Language Models (LLMs) are widely used for downstream tasks such as tabular classification, where ensuring fairness in their outputs is critical for inclusivity, equal representation, and responsible AI deployment. This study…
In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with…
In a co-simulation context, interconnected systems of differential equations are solved separately but they regularly communicate data to one another during these resolutions. Iterative co-simulation methods have been developed in order to…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…
Let $F:X\to X$ be a $C^2_\loc$ map in a Banach space $X$, and $A$ be its Fr\`echet derivative at the element $w:=w_\ve$, which solves the problem $(\ast) \dotw=-A^{-1}_\ve(F(w)+\ve w)$, $w(0)=w_0$, where $A_\ve:=A+\ve I$. Assume that…