1. Outline an algorithm for finding the eigenvalues of a reduced symmetric tridiagonal matrix the subdiagonal contains one or more zeros 2. Show that the algorithm with shift k,k fails, but the...

1.

Outline an algorithm for finding the eigenvalues of a reduced symmetric tridiagonal matrix
the subdiagonal contains one or more zeros

2.

Show that the
algorithm with shift

_k,k
fails, but the Wilkinson shift

Succeeds.

3.

Let

<sub>0

1

i−1

i

n</sub>
 be the Sturm sequence used by the bisection method, with

_i
 Show it is not possible that

_i−1
 and

_i
 in other words, there cannot be two consecutive zero values in the sequence. Hint: What does Equation 19.16 say about

_i
-2