Corpus ID: 237592696

Simple exponential acceleration of the power iteration algorithm

@article{Sha2021SimpleEA,
  title={Simple exponential acceleration of the power iteration algorithm},
  author={Congzhou M. Sha and Nikolay V. Dokholyan},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.10884}
}
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies on the idea that repeated multiplication of a randomly chosen vector x by the matrix A gradually amplifies the component of the vector along the eigenvector of the largest eigenvalue of A while suppressing all other components. Unfortunately, the power… Expand

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References

SHOWING 1-10 OF 18 REFERENCES
Implementation of the modified power iteration method to two-group Monte Carlo eigenvalue problems
Abstract In nuclear engineering field, the Monte Carlo method has been used to solve the eigenvalue or criticality problem for many years. The theoretical basis for solving the eigenvalue problem isExpand
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field ofExpand
Spectral graph theory
  • U. Feige
  • Zeta and 𝐿-functions in Number Theory and Combinatorics
  • 2019
With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shallExpand
Principal component analysis: a review and recent developments
  • I. Jolliffe, J. Cadima
  • Computer Science, Medicine
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2016
TLDR
The basic ideas of PCA are introduced, discussing what it can and cannot do, and some variants of the technique have been developed that are tailored to various different data types and structures. Expand
Vibration modes of large structures by an automatic matrix-reductionmethod
TLDR
This chapter discusses three-Dimensional Guidance Equations for Quasi-Optimum Space Maneuvers, which were proposed at the XV IAF Congress in 1965 and are still in use today. Expand
Graph similarity scoring and matching
We outline a class of graph similarity measures that uses the structural similarity of local neighborhoods to derive pairwise similarity scores for the nodes of two different graphs, and present aExpand
Python 3 Reference Manual
TLDR
This book is part of a brand new six-part series of Python documentation books, and for each copy sold $1 will be donated to the Python Software Foundation by the publisher. Expand
Matplotlib: A 2D Graphics Environment
Matplotlib is a 2D graphics package used for Python for application development, interactive scripting,and publication-quality image generation across user interfaces and operating systems
Array programming with NumPy
TLDR
How a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data is reviewed. Expand
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