Request TVM formula guidance

[Dieter]

(12-20-2014 05:47 AM)iMatt04bit Wrote:  I found an improvement for the Secant method where it will solve much faster:

Code:

x0 = x0 - fx0 * ((x0 - x1)/(fx0 - fx1));

This should follow the other line with similar code.

Hmm... looks like the usual formula for the Secant method to me. ;-)

(12-20-2014 05:47 AM)iMatt04bit Wrote:  Now the secant method decrements from both x0 and x1 points as it solves.

Determining if (and how fast) the iteration converges is a quite tricky subject. Using different forms of the TVM equation may drastically change this behaviour, so the version given in the 12C manual is not neccessarily the best choise. I also would reccommend a look at the Kahan paper linked below.

(12-20-2014 05:47 AM)iMatt04bit Wrote:  Min/max number of iterations to solve for 21 scenarios tested are:
Newton: 2,6 and Secant: 5,9

So Newton's method converges faster?

Looking at "results.txt" the initial guesses look very good. How do you evaluate these?

Here's a paper by W. Kahan (who contributed much of the mathematics used in HP's calculators since the mid-Seventies and most of the later iEEE754 floating point standard): Mathematics written in sand addresses several pitfalls and problems using floating point arithmetics on computers and calculators. Especially pages 14 ff. may be interesting here as they deal with financial calculators and problems at solving for the interest rate. The "A Penny for your Thoughts" example also demonstrates why using log1p instead of pow is a good idea. You may also want to read p. 17–22 concerning the convergence of the Newton resp. Secant method.

Dieter