SQL & PL/SQL :: Solve Equation With Newton-Raphson Method

Is it possible to solve an equation with the newton-raphson method with sql?

I have an equation f(x)=1-a/x**2, f(x)'= 2a/x**3
and want to solve x for several a's

The newton-raphson methos uses the derivation as next approximation:

xn2 = xn1 - f(x)/f(x)'

The result should be like this:

create table temp_res (a integer, res number);
insert into temp_res values(1, 1);
insert into temp_res values(2, 1.41421288939285);
insert into temp_res values(3, 1.73205078513617);
insert into temp_res values(4, 1.99999999999617);
insert into temp_res values(5, 2.23606797658102);
insert into temp_res values(6, 2.4494897130809);
insert into temp_res values(7, 2.64575095945042);
insert into temp_res values(8, 2.82842712474403);