© Haksun Li, PhD 2022
H. Li, PhDNumerical Methods Using Javahttps://doi.org/10.1007/978-1-4842-6797-4_4

4. Finding Roots of System of Equations

Haksun Li, PhD1  
(1)
Hong Kong, China
 
A root-finding algorithm for a system of multivariable equations can find the values of (x1, x2, …, xn) such that the values of the of n equations in the system equal 0.
$$ \left\{\begin{array}{c}{f}_1\left({x}_1,{x}_2,\dots, {x}_n\right)=0\\ {}{f}_2\left({x}_1,{x}_2,\dots, {x}_n\right)=0\\ {}\vdots \\ {}{f}_n\left({x}_1,{x}_2,\dots, {x}_n\right)=0\end{array}\right. $$

There can be no solution, one unique solution, or multiple solutions for the system. Systems of nonlinear equations can be solved numerically by Newton’s method that uses the first-order derivatives or the Jacobian, an extension of the Newton-Raphson method for single variable equation. The idea is also, ...

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