WP-34S Integration speed

[lrdheat]

Is there a way to balance accuracy with speed of integration on the 34S as with HP's that can integrate? The HP's give the user the ability to require, say, 4 significant digits of accuracy vs. the full 12 digits in order to arrive at a result in a significantly shorter amount of time. Can this be accomplished on the wonderful 34S?

[Marcus von Cube]

The integration routine is modeled after the IG routine from the HP 41 PPC ROM. It uses the display accuracy to determine the number of iterations by means of the x≈ Y comparison command. You can improve the integration speed by setting a different display mode such as FIX 4 or SCI 4.

[Paul Dale]

However, an integral that is approximately zero will hit a snag and will continue iterating long after it should.

Nobody like the Gauss-Kronrod quadrature I initially implemented which was fast and good for smooth functions but in no way adaptive.


- Pauli

[Dieter]

(02-22-2014 12:35 PM)Paul Dale Wrote:  However, an integral that is approximately zero will hit a snag and will continue iterating long after it should.

Pauli, I remember we had a discussion on this very topic some time ago, and I suggested a possible fix: compare the current value of \(\int f(x)\) with an approximation of \(\int |f(x)|\). It worked well with the examples we discussed then. Details can be found here, cf. message 6 ff.

This change was supposed to get implemented in v. 3460 resp. 3462. So I thought this issue had been resolved.

Dieter

[Paul Dale]

Sorry, Dieter is correct. We implemented a fix for the integral approaching zero. I'd just forgotten about it.


- Pauli

[Dave Hicks]

This thread was moved from the General forum by request.

[walter b]

χαιρε, Δρακων. Now it's where ο δημος will look for it.

d:-)

[Dieter]

(02-23-2014 09:42 PM)Paul Dale Wrote:  We implemented a fix for the integral approaching zero.

I see the fix got implemented, but one final improvement I posted back then still is missing (cf. last message in the mentioned thread). It's one single line that should be added:

Code:

        ...
        FC?C f_final        /* final iteration done? */
        x[approx]? Y        /* or convergence? */
             JMP int_done
        RCL/ r_SkAbs
        RCL/ r_deltau
        RCL/ r_ba4        <==  add this line
        ABS
        ...

Maybe it can be added with the next update.

Dieter

[Paul Dale]

Dieter, I must have missed that final improvement. Added now but not built.

- Pauli

[Marcus von Cube]

(02-27-2014 09:28 PM)Paul Dale Wrote:  Dieter, I must have missed that final improvement. Added now but not built.

My Job! Build 3530 is Committed to SVN...