Re: Successive Approximation
Charles,
thanks for this example, it ringed the nostalgic string in my mind - my RPN based calculator uses very similar concept for SOLVER application.
Re: Successive Approximation
With respect to your original equation, Charles:
a^3 + 5*a^2 = 20,
here is one solution (I think the other two are complex).
-(1/3)*[5 + {[-290 + (21600)^(1/2)]/2}^(1/3) + {[-290 - (21600)^(1/2)]/2}^(1/3)]
According to my calculator, that is approximately, 1.72457672763.
Dan
Re: Successive Approximation
Yes my program agrees Dan. though it gives an extra 4 digits at the end: 1848.
It did this in only 7 iterations, which makes the technique tolerable even for relatively simple equations. But I appreciate the satisfaction and insight gained in solving the challenging ones yourself.