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Metode Biseksi

ꟷNon Linear Equation
Introduction of Bisection Method
The Bisection Method give a proof of a
practical method to find roots of
equations by β€œbi section”.
Bisection Method is formulated
based on prior theories and has been
stated as β€œ f (x) be a continuous function on
the interval [a, b]. If f (a) and f (b)
have opposite signs, then there is
an 𝛼 ∈ [a, b] such that f (𝛼) = 0
with a < 𝛼 < b”.
There will be 3 possibilities from this equation :
β€’ If 𝑓 π‘Ž0 . 𝑓 π‘₯0 < 0, the root lies in π‘Ž0 and π‘₯0
β€’ If 𝑓 𝑏0 . 𝑓 π‘₯0 > 0, there is no root lies in π‘₯0
and 𝑏0
β€’ If 𝑓(π‘₯0 ) = 0, we’re already done since π‘₯0 is the
root of 𝑓 π‘₯ .
Root 𝛼
The value of 𝛼 can be approximation with midpoint
equation of interval [a0 , b0] ;
a0 + b 0
π‘₯π‘œ =
* assume that f (a) < 0, while
f (b) > 0, the other case being
handled similarly.
©First Group | Numeric Method | Mathematics Airlangga
University 2019
The red line shows the interval [an, bn].
For an example, we have made an C++
program to determine roots from the equation
©First Group | Numeric Method | Mathematics Airlangga
University 2019
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