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I am given f(x)=cosh(x) and asked to estimate f’(0.6) using Richardson Extrapolation to the highest possible accuracy. I computed the centered difference using h1=0.2 and h2=h1/2=0.1

I got

D(0.1)=0.6377152021 and

D(0.2)=0.6409064362

I plugged both in tothe formulas and supposedly the second formula gives and more accurate estimate than the first and the third formula gives a more accurate estimate than the previous 2

  1. D= 4/3 D(0.1) - 1/3 D(0.2) = 0.6366514574, O(h^4)

true error = 0.000334%

  1. D= 16/15 D(0.1) - 1/15 D(0.2) = 0.6375024532, O(h^6)

true error = 0.133%

  1. D= 64/63 D(0.1) - 1/63 D(0.2) = 0.6376645476, O(h^8)

true error = 0.159%

My question is how come the first formula (which is the least accurate out of the others) gives me the most accurate result compared to the true value f’(0.6)=0.6366535821 ?

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