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The documentation for newton_raphson_iterate says:
uintmax_t& max_iter
An optional maximum number of iterations to perform.
On exit, this is updated to the actual number of iterations performed.
There are two issues relating to max_iter:
max_iteris copied to a variablecount. After each Newton iteration, one is subtracted fromcount. Because of thedo {...} while (count && ...)structure of the Newton iteration, ifmax_iter = 0, rollover occurs, makingmax_iterfunctionally infinite.- If
0 < max_iter, running out of iterations exits the Newton loop as if the tolerance was met.
These two observations are demonstrated in the code below.
const auto fn = [](double x) { return std::make_pair(x * x - 3, 2 * x); };
std::uintmax_t iters;
std::cout << std::setprecision(16);
for (int count = 0; count < 10; count++) {
iters = count;
const double x0 = boost::math::tools::newton_raphson_iterate(fn, 10.0, 0.0, 100.0, 52, iters);
std::cout << "max_iters: " << count << " -- used_iters: " << iters << " -- x: " << x0 << std::endl;
}max_iters: 0 -- used_iters: 8 -- x: 1.732050807568877
max_iters: 1 -- used_iters: 1 -- x: 5.15
max_iters: 2 -- used_iters: 2 -- x: 2.86626213592233
max_iters: 3 -- used_iters: 3 -- x: 1.956460731776899
max_iters: 4 -- used_iters: 4 -- x: 1.74492093914502
max_iters: 5 -- used_iters: 5 -- x: 1.732098271119538
max_iters: 6 -- used_iters: 6 -- x: 1.732050808219183
max_iters: 7 -- used_iters: 7 -- x: 1.732050807568877
max_iters: 8 -- used_iters: 8 -- x: 1.732050807568877
max_iters: 9 -- used_iters: 8 -- x: 1.732050807568877
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