The goal of this tutorial is to use the power method described in the lecture.

NOTE: This tutorial is available in Swedish: MATLAB_TUTO5_Sv.pdf

Practice exercise 1:

Write a Matlab function that calculates the dominant eigenvalue (if such an eigenvalue exists) and a corresponding eigenvector x of the matrix A with the power method. The function must have the declaration:

function [lambda,x]=potensmetoden(A,x0,tol)

x0 is a "start" vector (a priori or initial values) and tol a tolerance for the stop condition $LaTeX: | x_{k+1} - x_k | ≤ \text{tol}$ . Test with matrices from previous tasks. If it does not work, explain why.

Practice exercise 2:

Write a Matlab function that calculates the eigenvalue that is closest to the number α (if such an eigenvalue exists) and a corresponding eigenvector x to the matrix A using the inverse power method. The function must have the declaration:

function [lambda,x]=inversapotensmetoden(A,x0,alpha,tol)

x0 is a "start" vector (a priori or initial values) and tol a tolerance for the stop condition $LaTeX: | x_{k+1} - x_k | ≤ \text{tol}$ . Test with matrices from previous tasks. If it does not work, explain why.