Except for signs, no elements of the matrix change for executions of the Francis iteration of degree two If is large, this creates a very slow algorithm. When lack of convergence is detected, the...

Except for signs, no elements of the

matrix

change for

executions of the Francis iteration of degree two

If

is large, this creates a very slow algorithm. When lack of convergence is detected, the situation can be resolved by replacing the Francis double shift by an exceptional shift after

iterations

Build a

version of this matrix, apply impdsqr

times, and then execute diag(A,-1) and A(1,25). Repeat the experiment by applying impdsqr 35 times and 100 times. Comment on the results.

The function eigb terminates if any
or

eigenvalue block fails to converge in a default of

iterations. In

it is noted that there are small sets of matrices where the Francis algorithm fails to converge in a reasonable number of iterations. Let

and apply eigb to

for

⁻⁶

Comment on the result. Does eig give results? If so, why