Accuracy of numsolve in TI, CASIO

03262021, 09:55 PM
Post: #2




RE: Accuracy of numsolve in TI, CASIO
Assuming calculator use centraldifference derivative formula, this might answer your question.
Is there a general formula for estimating the step size h in numerical differentiation formulas ? Example, estimate (ln(x))' at x=2: lua> function D(x,h) return (log(x+h)log(xh))/(2*h) end lua> for i=4,8 do print(i, D(2, 10^i)) end 4 0.5000000004168335 5 0.5000000000088269 6 0.5000000000143777 7 0.49999999973682185 8 0.49999999696126407 Interestingly, optimal h for this example is also about 1e5: At the cost of more computation, we can use bigger h, and extrapolate for slope. (similar to Romberg's integration, extrapolate from raw trapezoids, or rectangles) lua> h = 1e3 lua> d1 = D(2,h) lua> d2 = D(2,h/2) lua> d1, d2, d2+(d2d1)/3 0.500000041666615 0.5000000104167235 0.5000000000000929 

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Accuracy of numsolve in TI, CASIO  lrdheat  03262021, 07:35 PM
RE: Accuracy of numsolve in TI, CASIO  Albert Chan  03262021 09:55 PM
RE: Accuracy of numsolve in TI, CASIO  robve  03262021, 10:23 PM

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