相关论文: Convergence Analysis of Natural Power Method and I…

In this study, the global convergence properties of the Oja flow, a continuous-time algorithm for principal component extraction, was established for general square matrices. The Oja flow is a matrix differential equation on the Stiefel…

The power method is a classical algorithm with broad applications in machine learning tasks, including streaming PCA, spectral clustering, and low-rank matrix approximation. The distilled purpose of the vanilla power method is to determine…

Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of the discrete algorithm. To realize that, we view the…

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations.…

In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The $O(1/n)$-energy convergence of the proposed method is proven, where $n$ is the number of iterations. In…

This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…

This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the…

We consider streaming principal component analysis when the stochastic data-generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to…

Continuous time (CT) and discrete time (DT) linear time invariant (LTI) systems are commonly introduced through distinct mathematical formalisms, which can obscure their underlying dynamical equivalence. This tutorial presents a unified…

This paper studies the $J$-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space framework. This is the basis for variational…

Autonomous control systems use various sensors to decrease the amount of uncertainty under which they operate. While providing partial observation of the current state of the system, sensors require resources such as energy, time and…

This paper studies the benefits of pressure-robust discretizations in the scope of optimal control of incompressible flows. Gradient forces that may appear in the data can have a negative impact on the accuracy of state and control and can…

The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this…

We present a new power method to obtain solutions of eigenvalue problems. The method can determine not only the dominant or lowest eigenvalues but also all eigenvalues without the need for a deflation procedure. The method uses a functional…

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…

From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we…

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…

A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…

Deep Reinforcement Learning (DRL) has become a popular method for solving control problems in power systems. Conventional DRL encourages the agent to explore various policies encoded in a neural network (NN) with the goal of maximizing the…

In machine learning, a self-attention dynamics is a continuous-time multiagent-like model of the attention mechanisms of transformers. In this paper we show that such dynamics is related to a multiagent version of the Oja flow, a dynamical…