Boost
C++ Libraries
...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
This is an older version of Boost and was released in 2018. The current version is 1.89.0.
The examples demonstrate how to use the various tools for root finding.
We start with the simple cube root function cbrt
( C++ standard function name cbrt)
showing root finding without
derivatives.
We then show how use of derivatives can improve the speed of convergence.
(But these examples are only a demonstration and do not try to make the ultimate
improvements of an 'industrial-strength' implementation, for example, of boost::math::cbrt, mainly
by using a better computed initial 'guess' at cbrt.hpp).
Then we show how a higher root (fifth root) 5√ can be computed, and in root_finding_n_example.cpp a generic method for the nth root that constructs the derivatives at compile-time.
These methods should be applicable to other functions that can be differentiated easily.