Usé itération to determine the dominant eigenvalue and an associated eigenvector for the following systems of equations. 1 (a) (b) 2
Usé itération to determine the dominant eigenvalue and an associated eigenvector for the following systems of equations. 1 (a) (b) 2
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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![1. Use iteration to determine the dominant eigenvalue and an associated
eigenvector for the following systems of equations.
(a)
(b)
Use [1, 2] or [1, 2, 0] as your startrng vector. This means that for part
(a), you iterate the system
x = Lx, + 1x2
x½ = 0 + 2x2
Use the Raleigh quotient to refine your estimate of the dominant eigen-
value.
2. Repeat the iteration in Exercise 1 using the vector [1, 1] or [1, 1, 1] as
a starting vector. How does this affect the speed of convergence to the
dominant eigenvector? For one of the matrices, you do not converge to
the dominant eigenvector-why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0006be22-92b5-42a0-99d5-189f846984c8%2Fd26cf8df-782d-479a-ac55-1b9ebab21a71%2F8t552jn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Use iteration to determine the dominant eigenvalue and an associated
eigenvector for the following systems of equations.
(a)
(b)
Use [1, 2] or [1, 2, 0] as your startrng vector. This means that for part
(a), you iterate the system
x = Lx, + 1x2
x½ = 0 + 2x2
Use the Raleigh quotient to refine your estimate of the dominant eigen-
value.
2. Repeat the iteration in Exercise 1 using the vector [1, 1] or [1, 1, 1] as
a starting vector. How does this affect the speed of convergence to the
dominant eigenvector? For one of the matrices, you do not converge to
the dominant eigenvector-why?
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