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HP calcs are really not that accurate..
12-04-2017, 09:05 AM
Post: #61
RE: HP calcs are really not that accurate..
One must use the "Interval Newton Method" which isn't Newton's method converted to interval arithmetic (as I described above).

https://ww2.ii.uj.edu.pl/~zgliczyn/cap07/krawczyk.pdf
http://www2.math.uni-wuppertal.de/~xsc/xsc/node12.html

Starting with the interval (0,1) one computes x0=(0+1)/2; assuming the 0 and 1 are exact and that d is the unit of rounding, one uses F=x^3-2x+2 and dF=3x^2-2 starting at (0+1)/2 or 1/2 with the Newton formula:

(1/2-(3/8-1+2)/(3/4-2) giving (1/2-(11/8)/(-5/4)) => (1/2+(11/8)*(4/5)) => (1/2+11/10)=>(5/8+d,5/8-d). The last interval is intersected with (0,1) and the process continued. This assumes that I did my arithmetic correctly. The formulas are in the links.
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12-04-2017, 09:39 AM
Post: #62
RE: HP calcs are really not that accurate..
(12-04-2017 09:05 AM)ttw Wrote:  One must use the "Interval Newton Method" which isn't Newton's method converted to interval arithmetic (as I described above).

https://ww2.ii.uj.edu.pl/~zgliczyn/cap07/krawczyk.pdf
That's a bit disappointing.

Looking at your first reference (the pdf), the requirements on f ensure that is is injective. In the one-dimensional situation this implies (together with smoothness) that it must be strictly monotonic. This is very restrictive and even the simple example f(x)=x^3-2x+2 does not meet the requirement.
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12-04-2017, 04:20 PM
Post: #63
RE: HP calcs are really not that accurate..
(12-03-2017 11:18 PM)AlexFekken Wrote:  
(12-03-2017 08:05 PM)Claudio L. Wrote:  Sounds like a nice challenge... I'll start thinking about this, you might see it implemented in 6 months or so in... [that project I mentioned a million times].

By the way, I am serious enough to buy an HP 50g (while they are still reasonably priced) if you are serious about this. I assume you are talking about something like interval arithmetic in newRPL...?

So are you serious?

Serious I am. Overly optimistic with the time it will take... probably too. You don't need to buy a 50g, a 40gs will do for less money.
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12-04-2017, 10:38 PM
Post: #64
RE: HP calcs are really not that accurate..
(12-04-2017 04:20 PM)Claudio L. Wrote:  Serious I am. Overly optimistic with the time it will take... probably too. You don't need to buy a 50g, a 40gs will do for less money.

That's good enough for me and thanks for the tip. But I was looking for an excuse to add the legendary 50g to my collection anyway; before Australian prices will go through the roof as well.
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12-15-2017, 03:28 PM
Post: #65
RE: HP calcs are really not that accurate..
So, I've come to the conclusion that 34 significant digits should be OK.

My just arrived and unboxed DM42 were given the SQRT2 "torture test" with 10 SQRT's and squared back.
Display showing "2" as answer, though doing a "2 -" command resulted in "-2,8E-32.
I'm happy with that, and my Asperger/ADD have got peace of mind Smile

Esben
28s, 35s, 49G+, 50G, Prime, SwissMicros DM42
Elektronika MK-52 & MK-61
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