Re: Cube Root

["Andy Warren" <warrena@xxxxxxxxxxx>]

Well Walter's got his answer for the cube root, hopefully he's using RPGIV (higher math is painful without it.) If for whatever reason RPGIII is all you've got:

 

Richard Jackson's and Jim Langston's methods for the cube root are linear interpolation. Newton's method converges faster.

 

Newton's iterative formula for the cube root of r is:

 

x(n) = x(n-1) - (x(n-1) ** 3 - r) / 3*x**2(n-1)

 

where:
x(n) is the next approximation
x(n-1) is the previous approximation
x(0) is the initial guess

 

x(n-1)**3 = x(n-1) * x(n-1) * x(n-1)
x(n-1)**2 = x(n-1) * x(n-1)

 

We're lucky in that x**3 - r has only one (real) root, so plugging in any value except zero for the initial guess will work

 

--Andy

 

__________________________________________
Andrew H. Warren
Senior Systems Analyst
IBM Certified Specialist-RPGIV Developer
Ottaway Newspapers Inc.
Campbell Hall, New York
__________________________________________