# Exercise Solution 2.21

Details of this solution are available as an Excel spreadsheet.

The Jacobian of *f* is:

[s1]

Based upon this, we apply Newton’s method with line searches. Results are indicated below.

Exhibit s1: The process converges rapidly.

A line search was used to obtain *x*^{[3]}. Newton’s method originally determined *x*^{[3]} = (1.7515, 1.7636), which failed criterion [2.153]. Applying a line search, yielded λ^{*} = 0.1533. This corresponded to value *x*^{*} = (1.9619, 0.5525). We set *x*^{[3]} = *x*^{*}. This did satisfy criterion [2.153]. No other line searches were required.