1. Implement the Rayleigh quotient iteration described in Problem 19.18 in the MATLAB function rqiter. Using a random 0, test rqiter with random matrices of dimensions and Use tol maxiter 2. ...

1.

Implement the Rayleigh quotient iteration described in Problem 19.18 in the MATLAB function rqiter.

Using a random

₀, test rqiter with random matrices of dimensions

and

Use tol

maxiter

2.

Implement Newton’s method with a MATLAB function having calling syntax

root = newton(f,df,x0,tol,maxiter);

The argument f is the function, df is


x0 is the initial approximation, tol is the required relative

error bound

for all points except those very close to the pole at

Plot g

of the interval

Is there a root in the interval

Try to compute the root using Newton’s method with

₀

Explain the results.