Solution Found!
[M] Use the inverse power method to estimate the middle
Chapter 5, Problem 17E(choose chapter or problem)
Problem 17E
[M] Use the inverse power method to estimate the middle eigenvalue of the A in Example 3, with accuracy to four decimal places. Set
Reference Example 3:
It is not uncommon in some applications to need to know the smallest eigenvalue of a matrix A and to have at hand rough estimates of the eigenvalues. Suppose 21, 3.3, and 1.9 are estimates for the eigenvalues of the matrix A below. Find the smallest eigenvalue, accurate to six decimal places.
Questions & Answers
QUESTION:
Problem 17E
[M] Use the inverse power method to estimate the middle eigenvalue of the A in Example 3, with accuracy to four decimal places. Set
Reference Example 3:
It is not uncommon in some applications to need to know the smallest eigenvalue of a matrix A and to have at hand rough estimates of the eigenvalues. Suppose 21, 3.3, and 1.9 are estimates for the eigenvalues of the matrix A below. Find the smallest eigenvalue, accurate to six decimal places.
ANSWER:
Solution 17E
Step 1
The objective is to estimate the middle eigenvalue of the matrix:
Use MATLAB to find the list.
Code for MATLAB:
function [v,lamda] = IPM(B,tol)
tic;
A=inv(B);
n=size(A,1);
v=rand(n,1);
v=v/norm(v);
res=1;
while (res > tol)
W= A*v;
lamda=max(abs(W));
v= W/lamda;
res=norm(A*v-lamda*v);
toc
end