HP calcs are really not that accurate..

12042017, 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.uniwuppertal.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^32x+2 and dF=3x^22 starting at (0+1)/2 or 1/2 with the Newton formula: (1/2(3/81+2)/(3/42) giving (1/2(11/8)/(5/4)) => (1/2+(11/8)*(4/5)) => (1/2+11/10)=>(5/8+d,5/8d). 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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