1. 2. Use bidiag and convert to an upper-bidiagonal matrix. Carry out one downward sweep of the Demmel-Kahan algorithm. 3. The computation of singular values is well conditioned, but the same is...

1.

2.

Use bidiag and convert

to an upper-bidiagonal matrix.

Carry out one downward sweep of the Demmel-Kahan algorithm.

3.

The computation of singular values is well conditioned, but the same is not true of singular vectors. Singular vectors corresponding to close singular values are ill-conditioned. This exercise derives from an example in

and show that the right singular vectors of

are

be a perturbation of

Show that the right singular vectors of

are