Chapter 10, Problem 15P

Determine the condition number for the following system using the row-sum norm. Do not normalize the system.

$\left[\begin{array}{cccc}1& 4& 9& 16\\ 4& 9& 16& 25\\ 9& 16& 25& 36\\ \begin{array}{l}16\\ 25\end{array}& \begin{array}{l}25\\ 36\end{array}& \begin{array}{l}36\\ 49\end{array}& \begin{array}{l}49\\ 64\end{array}\end{array}\begin{array}{c}25\\ 36\\ 49\\ \begin{array}{l}64\\ 81\end{array}\end{array}\right]$

How many digits of precision will be lost due to ill-conditioning?

(b) Repeat (a), but scale the matrix by making the maximum element in each row equal to one.