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BISECTION METHOD

Prepared by

Md. Mujahid IslamMd. Rafiqul Islam

Khaza Fahmida Akter

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DEFINITION

The bisection method in mathematics isa rt findin! methd "hich repeatedly bisectsan inter#al and then selects a subinter#al in "hich a rt must lie fr further prcessin!.

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It is a #ery simple and rbust methd$ but it is

als relati#ely sl". %ecause f this$ it is ftenused t btain a ru!h appr&imatin t aslutin "hich is then used as a startin! pintfr mre rapidly cn#er!in! methds .Themethd is als called the binary search methd 

r the dichtmy methd.

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ALGORITHM

'tep () *hse t" appr&imatins A and %+%,A- such that

f+A-f+%-/0

'tep 1) 2#aluate the midpint * f 3A$%4 !i#en by 

*5+A6%-71

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8 'tep 9) If f+*-f+%-/0 then rename % : * as A :

%. If nt rename f * as % . Then apply thefrmula f 'tep 1.

8  'tep ;)'tp e#lutin "hen the different f t"successi#e #alues f * btained frm 'tep 1 is

numerically less than 2$ the prescribedaccuracy .

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GRAPHICALLY REPRESENTATION

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EXAMPLE

Given that, f  + x - 5 x 1 < 1. =ur task is findin! thert f this equatin.

 'lutin)

>et us start "ith an inter#al f len!th ne) a0 5 (

and b( 5 1. ?te that f  +a0- 5 f +(- 5 < ( / 0$

and f  +b0- 5 f  +1- 5 1 , 0. @ere are the first 10applicatins f the bisectin al!rithm)

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CODE IN C++

include/istream,include/cmath,usin! namespace stdB

define 2'P 0.000000(define f+&- &&<1int main+-Cduble &($&1$&9$A$%$*Bcin,,&(,,&1Bint i5(B

dC&95+&(6&1-71B A5f+&(-B%5f+&1-B*5f+&9-Bif+A*/0-C&15&9BDelse if+*%-C&(5&9BDi66BD"hile+fabs+*-,2'P-Bcut//&9BD

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CODE DESCRIPTION

8 @ere "e define #ariable type : functin type.

8 Input t" #alues "hich are l"est : hei!ht #aluef the functin .Then "e pass it thru!h

functin fr manipulatin .

8 Functin return result until itEs cnditin fulfill.

8 Finally "e !et result .

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SUMMARY

8 efinitin f %isectin methd : %asic

infrmatin f %isectin methd .8 Al!rithm f %isectin methd .

8 *alculate f rt by usin! by sectin methd "ith help f imprtant e&ample .

8 Representin! in pr!rammin! >an!ua!e .

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QUESTION & SUGGESTION

 Any Guestin H

Please i#e yur su!!estin r ad#ice "hich is #ery helpful t create a better presentatin .

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THANKS TO ALL