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 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 itdoes 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 inthis question.As a reminder, we assumed |A1| > |A2| > |A3| > · · · > |An|· Step-11NOWep 3(A-61)V₁ = AVI-AV= A₁V₁-66V₁= (-6) V₁.A-6 is Eigen value for CA-64)Similarly 12-6, 3-6,stepilNOWeigen values for (A-61)"A₁-6дот 6 areEigen values of (A-61)¹ㅗ25612-6are

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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

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