theorem: suppose that & is the root of f(x) = 0 and / f, f , f in a neighbourhood & such as I are continuous and fix) to Vne I, in this case if nitial approximations are close enough to of the generated sequence fxça defined 1=0 secant formula is convergent to d- with lim lentil = C Tejp in the other words the convergence √5+1 2 oder is p 1,6 (‡o P=-

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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theorem: suppose that & is the root of f(x) = 0 and
1
f, f , f in a
neighbourhood & such as I
are continuous and f(x) to Vine I, In this case
if initial approximations
are close enough to of
the generated sequence {xas defined by
1=0
secant formula is convergent to d.
with lim lent!! =C
lepp
in the other words the
convergence
(‡o P=
√5+1
2
order is p≈ 1,6
M
Transcribed Image Text:theorem: suppose that & is the root of f(x) = 0 and 1 f, f , f in a neighbourhood & such as I are continuous and f(x) to Vine I, In this case if initial approximations are close enough to of the generated sequence {xas defined by 1=0 secant formula is convergent to d. with lim lent!! =C lepp in the other words the convergence (‡o P= √5+1 2 order is p≈ 1,6 M
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