f = x^2 - 16
fp = 2*x
exact = 4
# f = tan(x/4)-1
# fp = sec(x/4)^2/4
# exact = pi
(plot(f,(x,0,5))+plot(fp,(x,0,5),color='green')).show()
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x0 = 20
points = plot(f,(x,0,5))
points += point((x0,0),color='red',size=40)
show(points)
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p = x0
errors = []
for k in range(6):
fx = f(x=p)
fxp = fp(x=p)
p = p - fx/fxp
points += point((p,0),color='red',size=40)
errors.append(n(abs(p-exact)/exact))
end
show(points)
pretty_print((p,fx))
pretty_print(' or ',(n(p),n(fx)))
pretty_print(errors)
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Experimentally determine the rate of convergence
# Experiment with r to see if there is a (relatively) constant value for the following ratio of successive error terms
r = 2
for k in range(len(errors)-1):
errors[k+1]/errors[k]^r
0.192307692307692 0.335051546391753 0.462446824116180 0.498479875456300 0.499997682185350 0.192307692307692 0.335051546391753 0.462446824116180 0.498479875456300 0.499997682185350 |
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