Comparing Three Ways to Find the Roots of a Mathematical Equation

For my research comparing the three ways to find the roots of the mathematics, we study, analyze and compare three different ways to find the roots of the equation. It will include a way to rearrange the "Symbol modification method", "Newton-Raphson method", and finally "f (x) = 0" into the form of "x = g (x)". Since we use these methods to find the roots of the equation we compare the advantages and disadvantages of this method with each other. Analyze which is best based on factors such as convergence speed and available software and ease of use of hardware.

The mathematical method is a special case of the principle that pure abstraction and intellectual methods are not patentable. Therefore, mathematical methods such as calculation methods, equations, square root, cube root, and all other similar mental skill behavior are not patentable. Likewise, just manipulating abstract concepts without specifying actual applications or solving pure mathematical problems / equations is not included in this category. However, in order to clearly specify the range of protection required in the present invention, there are numerical expressions only in the claims, which are not necessarily claims of "mathematical expression". Furthermore, such exclusion can not be applied to inventions which include mathematical expressions and which result in an encoding system which reduces noise in a communication / electric / electronic system or encryption / decryption electronic communication.

See my previous blog, I've released it as a mathematical optimization update equation before. Finding the root of the equation is the Newton-Raphson method. Since cost is always defined as a positive real-valued function, I think that this method is mainly suitable for minimizing machine learning. But someone pointed out the updated equation of the Newton - Raphson method, I continue to use this equation because I give the smoothest curve I'm going to do here. Stein's space-time analogy: cost dimension is related to the dimension of all parameters)