Step 3. Compute the derivative df/d61 of f with respect to 81. A numeric approximation of this derivative is given by


 df/de1 = (f(E1+68El) -f(E1)]/681, (6.27)


where S8 is a small increment of 81. Note that this

approximation requires another function evaluation at

(E1+6E1).

 Step 4. Obtain a new estimate for 01 by the onedimensional Newton-Raphson method, i.e.


 e1(new) 81 f(81)/(df/d01). (6.28)


 Steps 2 to 4 must be repeated until 1el is obtained to the desired accuracy. The solution set can then be completed by using the values of 82, e3 and 04 as computed at the last iteration and by computing 05 uniquely from


 C5

 R5x = S5 = R4-1 R3-1 R2-1 RI- m.

 0

and

 85 = atan2(S5,C5).


 The one-dimensional method just described is flexible in terms of the choice of function f to be used. A

different function can be implemented. The only

requirements are that f(91) be computable for any value of

..