To numerically find a root of , we may use the Newton’s method. Assuming the root is at the proximity of , to find a better approximate , we consider the tangent line at , which is provided by the equation

Thus the -intercept of such tangent, , reveals an approximation closer than , i.e. the formula for Newton’s method is

In case of a function , we may find its zero by the following. At an approximated zero ,

is a hyperplane tangent to at , so the refinement would be

For a more general function, , at an approximated zero , the tangent hyperplane is

where is the Jacobian operator, which if


So the formula would be