Power method to determine largest real eigenvalue does not converge
显示 更早的评论
I have written a function as per the pseudocode to determine the maximum eigenvalue of a given nxn matrix given a specified tolerance value. Unfortunately my anwser does not converge. The vector seems to be unchanged after the first 50-60 iterations so i attempted to caclulate the eigenvalue at the 55th iteration by calculating the infinite norm of the corresponding vector. The anwser is not close at all. Any assistance would be appreciated (i have attached the pseudocode as a PNG).
% M = randi(15,5)/10;
% A = M'*M;
A = [1 2 1; 6 -1 0; -1 -2 -1];
[V,D] = eig(A)
[e,v]= power_method(A,1e-4)
function [eigen_value,vector]= power_method(A,tol)
% Write you code here
x0 = randi([1,5],length(A),1); %arbitrary vector x0
vector = x0; %start with arbitrary vector x0
iter = 1; %iteration counter
while 1
vector_old = vector;
vector = A*vector;
eigen_value = norm(vector,inf);
vector = vector/max(vector);
error = norm(vector - vector_old);
if error<tol
break
end
iter = iter + 1;
end
iter
error
end
回答（1 个）
Bruno Luong
2021-3-28
The png is not correct if A has negative largest eigan (absolute) value
Try this
A = [1 2 1; 6 -1 0; -1 -2 -1];
[V,D] = eig(A)
[e,v]= power_method(A,1e-4)
function [eigen_value,vector]= power_method(A,tol)
% Write you code here
x0 = randi([1,5],length(A),1); %arbitrary vector x0
vector = x0; %start with arbitrary vector x0
iter = 1; %iteration counter
while 1
vector_old = vector;
vector = A*vector;
[~,imax] = max(abs(vector));
maxv = vector(imax);
vector = vector/maxv;
error = norm(vector - vector_old);
if error<tol
break
end
iter = iter + 1;
end
eigen_value = maxv
iter
end
类别
在 帮助中心 和 File Exchange 中查找有关 Eigenvalues & Eigenvectors 的更多信息
2021-3-28
2021-3-28
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
