The Jacobi diagonal preconditioner (Problem 21.7) performs best when the coefficient matrix is strictly diagonally dominant and has widely varying diagonal entries. Write a function jacobipregmres...

The Jacobi diagonal preconditioner (Problem 21.7) performs best when the coefficient matrix is strictly diagonally dominant and has widely varying diagonal entries. Write a function jacobipregmres that implements Jacobi preconditioning for the

method. Return with a message if the preconditioned matrix does not have a condition number that is at most 80% of the condition number for

Build the

matrix,

with seven diagonals:

Compute the condition number of

Using

^T

tol
⁻⁶

and

compute the solution using both gmresb and jacobipregmres. Display the residuals.