Lecture 3 Printed Notes

Lecture 3 Printed Notes - ME...

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!"#$% "’()’**+)’( ,-./0121)-’23 !*14-56 7*810+* 9-1*6 :7*810+* ;*1 9-< => !*14-56 ?-+ ;-3@)’( 9-’3)’*2+ "A021)-’6 2. False Position (Regula – Falsi) Method Here obtain [ x L , x R ], such that f(x L ) . f(x R ) <0. Instead of successively bisecting the interval, as in the bisection method, linear interpolation is used to obtain x App such that ( x App , 0) lies on the line joining ( x L , f(x L ) ) and ( x R , f(x R ) ). Since, the points ( x L , f(x L ) ), ( x App , 0) and ( x R , f(x R ) ) all lie on the same line, it is clear that: L R L App L R L x x x x x f x f x f ! ! " ! ! ) ( ) ( ) ( 0 , and hence, ) ( ) ( ) ( R L R L L L App x f x f x x x f x x ! ! ! " . Next we determine which of the 2 sub-intervals [ x L , x App ] or [ x App , x R ] contains the root of f(x) . Algorithm: Given the above, REPEAT ) ( ) ( ) ( R L R L L L App x f x f x x x f x x ! ! ! " IF f(x L ) . f(x App ) <0, THEN x R = x App ELSE x L = x App UNTIL Stopping criteria are met END Possible stopping criteria
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Lecture 3 Printed Notes - ME...

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