5. To find the value of x when u is given, i.e. to find the value of
[theta] when u_([theta]) is given, we use the same formula as for
direct interpolation, but proceed (if differences beyond the first are
involved) by successive approximation. Taylor's Theorem, for instance,
gives
[theta]
[theta] = (u_[theta] - u0) / (c1 + c2 + ------- + ...)
2!
= (u_[theta] - u0) / P1 (6),
We first find an approximate value for [theta]: then calculate P1, and
find by (6) a more accurate value of [theta]; then, if necessary,
recalculate P1, and thence [theta], and so on.