Home > Matrix Algebra calculators > Power Method for dominant eigenvalue calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find power method for eigenvalue [[8,-6,2],[-6,7,-4],[2,-4,3]]

Solution:
Your problem `->` power method for eigenvalue [[8,-6,2],[-6,7,-4],[2,-4,3]]


 `A=` 
8-62
-67-4
2-43


 `x_0=` 
1
1
1


`1^(st)` Iteration

 `A x_0 =` 
8-62
-67-4
2-43
 
1
1
1
 `=` 
4
-3
1


and by scaling we obtain the approximation
`x_1=``1/4`
4
-3
1
`=`
1
-0.75
0.25


`2^(nd)` Iteration

 `A x_1 =` 
8-62
-67-4
2-43
 
1
-0.75
0.25
 `=` 
13
-12.25
5.75


and by scaling we obtain the approximation
`x_2=``1/13`
13
-12.25
5.75
`=`
1
-0.9423
0.4423


`3^(rd)` Iteration

 `A x_2 =` 
8-62
-67-4
2-43
 
1
-0.9423
0.4423
 `=` 
14.5385
-14.3654
7.0962


and by scaling we obtain the approximation
`x_3=``1/14.5385`
14.5385
-14.3654
7.0962
`=`
1
-0.9881
0.4881


`4^(th)` Iteration

 `A x_3 =` 
8-62
-67-4
2-43
 
1
-0.9881
0.4881
 `=` 
14.9048
-14.869
7.4167


and by scaling we obtain the approximation
`x_4=``1/14.9048`
14.9048
-14.869
7.4167
`=`
1
-0.9976
0.4976


`5^(th)` Iteration

 `A x_4 =` 
8-62
-67-4
2-43
 
1
-0.9976
0.4976
 `=` 
14.9808
-14.9736
7.4832


and by scaling we obtain the approximation
`x_5=``1/14.9808`
14.9808
-14.9736
7.4832
`=`
1
-0.9995
0.4995


`6^(th)` Iteration

 `A x_5 =` 
8-62
-67-4
2-43
 
1
-0.9995
0.4995
 `=` 
14.9962
-14.9947
7.4966


and by scaling we obtain the approximation
`x_6=``1/14.9962`
14.9962
-14.9947
7.4966
`=`
1
-0.9999
0.4999


`7^(th)` Iteration

 `A x_6 =` 
8-62
-67-4
2-43
 
1
-0.9999
0.4999
 `=` 
14.9992
-14.9989
7.4993


and by scaling we obtain the approximation
`x_7=``1/14.9992`
14.9992
-14.9989
7.4993
`=`
1
-1
0.5


`:.` The dominant eigenvalue `lamda=14.9992~=15`

and the dominant eigenvector is :
`=`
1
-1
0.5
`~=`
1
-1
0.5







Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

Share with your friends, if solutions are helpful to you.
 
Copyright © 2019. All rights reserved. Terms, Privacy





We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more