2c) Set σ = √₂ + min(|A2 − A3|, |A1 − A2|)/3. If you run power iteration on (A-oI)-¹, what will the algorithm converge to (assuming that it does converge successfully)? Hint: the largest eigenvalue of A is λ₁, the largest eigenvalue of A-¹ is the largest eigenvalue of (A - αI) is λ; – a with the farthest X; farthest a, the largest eigenvalue of (A — aI)-¹ is with the closet X; to a. Think about what the largest eigenvalue of the matrix is in this question. As a reminder, we assumed |A1| > |A2| > |A3| > · · · > |An|-
2c) Set σ = √₂ + min(|A2 − A3|, |A1 − A2|)/3. If you run power iteration on (A-oI)-¹, what will the algorithm converge to (assuming that it does converge successfully)? Hint: the largest eigenvalue of A is λ₁, the largest eigenvalue of A-¹ is the largest eigenvalue of (A - αI) is λ; – a with the farthest X; farthest a, the largest eigenvalue of (A — aI)-¹ is with the closet X; to a. Think about what the largest eigenvalue of the matrix is in this question. As a reminder, we assumed |A1| > |A2| > |A3| > · · · > |An|-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Previous question: 2b)
What are the eigenvalues of (A−σI)−1?
Hint: Your answer should involve σ and λj (for j=1,⋯,n). First, find eigenvalues of A−σI. Then take advantage of the fact that eigenvalues of A−1 are 1λj (for j=1,⋯,n).
Answer provided
Transcribed Image Text:2c)
Set o = √₂ + min(|A2 − A3|, |A1 – A2|)/3. If you run power iteration on (A — σ1)−¹, what will the algorithm converge to (assuming that it
does converge successfully)?
Hint: the largest eigenvalue of A is ₁, the largest eigenvalue of A-¹ is the largest eigenvalue of (A − aI) is λ; – a with the farthest X;
farthest a, the largest eigenvalue of (A — α¹)−¹ is with the closet X; to a. Think about what the largest eigenvalue of the matrix is in
this question.
As a reminder, we assumed |A1| > |A2| > |A3| > · · · > |An|·
Transcribed Image Text:Step-11
NOW
ep 3
(A-61)V₁ = AVI-AV
= A₁V₁-66V₁
= (-6) V₁.
A-6 is Eigen value for CA-64)
Similarly 12-6, 3-6,
stepil
NOW
eigen values for (A-61)
"
A₁-6
дот 6 are
Eigen values of (A-61)¹
ㅗ
256
12-6
are
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