|Re: Root Finding and the 11C|
Message #11 Posted by Les Wright on 30 Jan 2007, 6:58 a.m.,
in response to message #9 by Les Wright
I tried it out, and found that, alas, on the 33C, zero means zero internally, not the displayed value.
This equation turns up in Acton's Numerical Methods that Usually Work. On the 33C:
ENTER, x^2, 1, +, 2, /, 29.672, /, -
This fits just barely after the 34 step routine on the 33C, though I guess one could save steps by prestoring the constant 29.672.
This is basically a quadratic with two real roots, approx 0.017 and 59.3. If you start with a guess of 31, the routine won't converge but will wiggle back and forth between 59.32714430 and 59.32714429. Start with a better guess of 59.3, and the routine stops at the correct 10-digit root of 59.32714431. If the 33C had a RND function, the routine could be made to stop by setting FIX 7.
The rounding error can be fussy. If I start with the ostensibly even better guess of 59.327, I get the same wiggling as I got with a starting guess of 31. But if I choose an even worse guess of 30, it converges and stops at 59.32714431!
Weird. (Actually, not weird, as I know it has to do with how the rounding error accumulates according to how the root is approached.)
Thanks for sharing these amazing little routines. I note that they are half the length of the routine in the 11C manual, and I think are more efficient.