Optimization::RootBrent Function

Finds a root (zero) of a single variable function.

What it computes. Locates a root x^* of a real function of
one variable on the bracket [a_x,b_x] using Brent's method (the algol-60 zeroin: inverse quadratic interpolation and the secant rule, each step guarded by bisection). For the example objective

f(x) = x^3 - 2x - 5

Domain. a_x,b_x are finite reals; if b_x < a_x they are
swapped internally, so the order of the bracket does not matter. Func must change sign across the bracket, that is f(a_x) * f(b_x) <= 0. MaxIter > 0 caps the iterations; Accuracy ≥ 0 is the desired position tolerance.

Defined behaviour. Returns the iteration count and writes the root
to RootX. The convergence floor is 2 epsilon |x| + Accuracy/2, so Accuracy = 0 iterates to full machine precision - unlike Optimization::MinBrent, whose floor is sqrt(epsilon) |x| because a smooth minimum is numerically flat within that distance and a sign change is not. StopReason is TOptStopReason::OptResConverged when the bracket shrank below the tolerance or the function returned an exact zero, TOptStopReason::OptResNotFound when Func does not change sign across the bracket (no root is enclosed, and RootX is NAN),

TOptStopReason::OptResMaxIter when the iteration cap was hit,
TOptStopReason::optNANValue if the objective returned NaN, and
TOptStopReason::optStopped if the search was interrupted through
TOptControl. No exception is raised for a missing bracket: the

result is reported through StopReason.

Finds the root of a function of one variable. This routine uses a slightly modified version of the algol 60 procedure zero, introduced by Richard Brent.

Finds a root of single variable function by using default settings and no log.

Use this version if algorithm step logs are not needed.