Solution Found!
Solved: [M] Exercises 7–12 require MATLAB or other
Chapter 5, Problem 8E(choose chapter or problem)
[M] Exercises 7-12 require MATLAB or other computational aid. In Exercises 7 and 8 , use the power method with the \(\mathbf{x}_0\) given. List \(\left\{\mathbf{x}_k\right\}\) and \(\left\{\mu_k\right\}\) for \(k=1, \ldots, 5\).
\(A=\left[\begin{array}{ll}2 & 1 \\ 4 & 5\end{array}\right], \mathbf{x}_0=\left[\begin{array}{l}1 \\ 0\end{array}\right]\)
Questions & Answers
QUESTION:
[M] Exercises 7-12 require MATLAB or other computational aid. In Exercises 7 and 8 , use the power method with the \(\mathbf{x}_0\) given. List \(\left\{\mathbf{x}_k\right\}\) and \(\left\{\mu_k\right\}\) for \(k=1, \ldots, 5\).
\(A=\left[\begin{array}{ll}2 & 1 \\ 4 & 5\end{array}\right], \mathbf{x}_0=\left[\begin{array}{l}1 \\ 0\end{array}\right]\)
ANSWER:Solution 8E
Step 1
The objective is to find the list of using power method for the following matrix:
Use MATLAB to find the list.
Code for MATLAB:
function[x,lambda]=powermat(A,x0,nit) x = x0; for n=1:nit xnew = A*x; lambda = norm(xnew,inf)/norm(x,inf); fprintf('n = %4d lambda = %g x = %g %g %g \n', n, lambda, x');
x=xnew; end x=x/norm(x);%normalise x fprintf('n = %4d normalised x = %g %g %g\n', n, x');