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Let u be randomly chosen vector in R³. Set and for k> 0 set 20 |||v|| ' A-¹æk ||A-¹æk||' Xo = xo A-¹xo Ak+1 = Xk+1¹A-¹Xk+1 #k+1= i. What are the eigenvalues of A-¹? ii. What number do you expect A to converge to? 1 iii. What number do you expect to converge to? Xk iv. For large k, æ, is approximately an eigenvector corresponding to which eigenvalue of A?

Let u be randomly chosen vector in R³. Set and for k> 0 set 20 |||v|| ' A-¹æk ||A-¹æk||' Xo = xo A-¹xo Ak+1 = Xk+1¹A-¹Xk+1 #k+1= i. What are the eigenvalues of A-¹? ii. What number do you expect A to converge to? 1 iii. What number do you expect to converge to? Xk iv. For large k, æ, is approximately an eigenvector corresponding to which eigenvalue of A?

Advanced Engineering Mathematics
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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 Suppose the 3 × 3 matrix A has eigenvalues λ1 = −6, λ2 = −2, and λ3 = 5.

 

Let v be randomly chosen vector in R³. Set and for k> 0 set xo = V |||v|| ' Ak ||A-¹æk ||' Xo = xo¹ A-¹xo T Xk+1 = Xk+^A-1Xk+ Xk+1 = i. What are the eigenvalues of A-¹? ii. What number do you expect A to converge to? 1 iii. What number do you expect to converge to? Xk iv. For large k, æ is approximately an eigenvector corresponding to which eigenvalue of A? (3) (4)
Transcribed Image Text:Let v be randomly chosen vector in R³. Set and for k> 0 set xo = V |||v|| ' Ak ||A-¹æk ||' Xo = xo¹ A-¹xo T Xk+1 = Xk+^A-1Xk+ Xk+1 = i. What are the eigenvalues of A-¹? ii. What number do you expect A to converge to? 1 iii. What number do you expect to converge to? Xk iv. For large k, æ is approximately an eigenvector corresponding to which eigenvalue of A? (3) (4)
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