AI & ML
An Accelerated Power Method
arXiv cs.NA0 views
arXiv:2611.13283v1 Announce Type: new Abstract: An Accelerated Power Method (APM) for locating the dominant eigen-pair of a real, symmetric matrix is presented. The algorithm is motivated by Nesterov's Accelerated Gradient Method (AGM) and a connection between the APM and the AGM holds, that is analogous to the relationship between the Conjugate Gradient and Lanczos methods. Theoretical convergence analysis shows that the APM is guaranteed to recover the dominant eigen-pair of a normalized semi-definite matrix at a rate no worse than the Power Method. For normalized indefinite matrices, the APM will recover an extremal eigen-pair, but not necessarily the dominant one, and the rate can be worse than the vanilla PM, depending upon the choice of acceleration parameter. Computational practicalities are discussed, including parameter tuning, and numerical experiments are also presented.
Source：https://arxiv.org/abs/2611.13283PreviousBlock-Sparse Gauss-Newton Optimization of Finite Basis Physics-Informed Neural Networks: Sparse Automatic Differentiation ApproachNextA Second-Order Parallel Neumann-Robin Splitting for the Stokes-Biot System with a Linear Time-Step Restriction
Related posts
I wanted one screen that said whether a kids' app was worth installing
0dev.to
Before I Could Build GPT, I Had to Teach a Machine to Learn
0dev.to
Cogent and OpenAI build cyber defense factories for enterprises
0OpenAI Blog
ChatGPT Plus for veterans and servicemembers
0OpenAI Blog
Hitting 200 Strokes: What the Signature Maker Does at Its Stroke Limit
0dev.to
A Lightweight, Open-Source Network Digital Twin Blueprint for IoT-Edge Environments
0arXiv cs.NI