08-Bisection-Method-4UP - IVT Bisection method Examples Implementation details IVT Bisection method Examples Implementation details The Bisection Method

# 08-Bisection-Method-4UP - IVT Bisection method Examples...

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IVTBisection methodExamplesImplementation detailsThe Bisection MethodDhavide AruliahUOITMATH 2070Uc D. Aruliah (UOIT)The Bisection MethodMATH 2070U1 / 16IVTBisection methodExamplesImplementation detailsThe Bisection Method1The Intermediate value theorem2The Bisection method3Examples4Implementation detailsc D. Aruliah (UOIT)The Bisection MethodMATH 2070U2 / 16IVTBisection methodExamplesImplementation detailsThe Intermediate value theoremTheorem (Intermediate value theorem)Given a continuous function f:[a,b]Rsuch that f(a)f(b)<0, thenthere exists at least oneξ(a,b)such that f(ξ) =0.xyy=f(x)ab(a, f(a))(b, f(b))(ξ1,0)(ξ2,0)(ξ3,0)(ξ4,0)c D. Aruliah (UOIT)The Bisection MethodMATH 2070U4 / 16IVTBisection methodExamplesImplementation detailsBracketing a zeroAssumefis a continuous functionAny interval[a,b]for which eitherf(a)>0 andf(b)<0; orf(a)<0 andf(b)>0is said tobracketa zero offInterval can be called abracketEquivalent criterion:f(a)f(b)<0Assumption of continuity essential for interval to bracket a zeroc D. Aruliah (UOIT)The Bisection MethodMATH 2070U5 / 16
IVTBisection methodExamplesImplementation detailsExample: estimating2Letf