inclass11-eigen - [1/3 Objectives In-class work eigen...

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3/15/2016 [1/3] Objectives - In-class work: eigen - RELATE https://relate.cs.illinois.edu/course/cs357-sp16/flow-session/97658/0/ 1/1 Objectives Long-term goal: Understand the nature of eigenvectors and eigenvalues Understand how to apply Power Iteration and it's variants See an application of eigenvector extraction
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3/15/2016 [2/3] Inverse Iteration with a Shift - In-class work: eigen - RELATE https://relate.cs.illinois.edu/course/cs357-sp16/flow-session/97658/1/ 1/1 Inverse Iteration with a Shift Suppose is an matrix with the eigenvalues , and . Suppose you apply the following iterative algorithm: and choose . Assuming that the algorithm converges on an eigenvector, which eigenvalue of is associated with that eigenvector? A 4×4 −8,−6,5 1 xk+1=(A−σI)−1xk (A−σI)−1xk σ=4 A
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3/15/2016 [3/3] Principal Component Analysis (PCA) - In-class work: eigen - RELATE https://relate.cs.illinois.edu/course/cs357-sp16/flow-session/97658/2/ 1/1 Principal Component Analysis (PCA)
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