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System of Non-Linear Equations

A system of non-linear equations is a finite set of non-linear equations in a finite number of variables. A system of non-linear equations is also referred to as a non-linear system. We can write a non-linear system of equations in NN variables and MM equations as follows:

f1(x1,x2,...,xN)=0f2(x1,x2,...,xN)=0⋯fM(x1,x2,...,xN)=0f_1(x_1, x_2, ..., x_N) = 0\\ f_2(x_1, x_2, ..., x_N) = 0\\ \cdots\\ f_M(x_1, x_2, ..., x_N) = 0

A non-linear system may have one or more than one solutions. Sometimes it might not even have any solutions. In this article, we will learn about an extension of Newton-Raphson's method for solving a non-linear system.