wowo0709

wowo0709

큰 사람이 되려면 큰 물에서 놀아라

[NumericalAnalysis] Eigen Problems 2

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Power Iteration

Setup

image-20211109172738708


Usual Trick

image-20211109172755258


Power Iteration

image-20211109172822482


Normalized Power Iteration

image-20211109172846013



Other Eigenvalues

Eigenvalues of Inverse Matrix

image-20211109172948664


Eigenvalues of Shifted Matrix

image-20211109173015466


Summary

image-20211109173042879



Multiple Eigenvalues

Unlikely Failure Mode for Iteration

image-20211109173130203


Solution

image-20211109173147323



QR Iteration

Similarity Transformations

image-20211109173229237


Transformation without Inversion

image-20211109173254833


QR Iteration

image-20211109173316344


Example

image-20211109173344916



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