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.