1. METHODS TO FIND ROOTS OF EQUATION FIXED POINT, NEWTON – RAPHSON, SECANTE JONATHAN PEREZ UIS

2. CLOSE METHODS BISECCION

3. BISECCION + y=f(x) Raíz - f(xs) xi xs Biseccion

4. TheObjective of thisMethodconsist in divide theintervaltothehalf, lookingfowardforthechange of sing. If f(x) is real and continous in theintervalthatgoesfromxitoxsand f(xi) ∗ f(xs)<0, thenthereis at least 1 rootbetweentheintervals(xi) , (xs) . Biseccion

5. + y=f(x) xr=xi+xs2 Raíz - f(xs) xi xs Biseccion

8. xs=still the same Biseccion

9. ERROR FOR THE NEW RESULT Ea=xr now−xr lastxr now ∗100% EXAMPLE: Calculatetheroot of thenextequation. fx=663.38x1−e−0.146843x−40. Evaluatedbetweenvalue of 12 – 16 , with tol= 0.2 Biseccion

10. In thetable, we can seethatthevalue in the 7th iterationis 14. 76, whichisapproximatetothe real valueswhithan error of 0.1058 Biseccion-Example

11. CLOSE METHODS FALSE POSITION

12. FALSE POSITION Ifwecosiderthisgrafic: if instead of considering the midpoint of the interval, we take the point where this line crosses the axis, we come close faster root-this is in itself, the central idea of the rule method false and this is really the only difference with the method of bisection, as in all other respects the two methods are practically identical. Raíz Verdadera Raíz Falsa

13. So, ifyou can see, thismethodisthesamethatthebiseccion, thenweneedfind a xr, it’ll be give by: Raíz Verdadera Raíz Falsa FALSE POSITION

14. Example weneedsearchtherootsfor; x3+4x2−10 Evaluatedfromvalues 1-2, withtolerance = 0.01 FALSE POSITION

15. In thetable, we can seethatthevalue in the 6th iterationis 1.3652, whichisapproximatetothe real valueswhithan error of 0.005829 FALSE POSITION

17. METODOS NUMERICOS PhD EDUARDO CARRILLO – UNIVERSIDAD INDUSTRIAL DE SANTANDER 2010

18. CHAPRA, Steven C. “Métodos Numéricos para Ingenieros”. Edit. McGraw Hil.