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# Muller method

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### Muller method

1. 1. 1<br />MULLER METHOD<br />Jeannie Castaño 2053298<br />
2. 2. This is a method to find the roots of equations polynomials in the general way: <br /> Where n is the order of the polynomial and they are they constant coefficients. Continuing with the polynomials, these they fulfill the following rules: <br />" For the order equation n, is n real or complex roots. It should be noticed that those roots are not necessarily different. <br />" If n is odd, there is a real root at least. <br />" If the complex roots exist, a conjugated couple exists.<br />
3. 3. DEFINITION<br />It is the method secant, which obtains roots, estimating a projection of a direct line in the axis x, through two values of the function.<br />The method consists on obtaining the coefficients of the three points, to substitute them in the quadratic formula and to obtain the point where the parable intercepts the axis x. <br />
4. 4. f(x)<br />Línea recta<br />x<br />Raíz estimada<br />x<br />x<br />X<br />X1<br />X0<br />Raíz <br />
5. 5. Raíz estimada<br />f(x)<br />Parábola<br />0<br />0<br />0<br />Raíz <br />x<br />x<br />X<br />X2<br />X0<br />X1<br />This way, this parable is looked for intersectorthe three points [x0, f(x0)], [x1, f(x1)] and [x2, f(x2)]. <br />
6. 6. The last equation generates that , this way, one can have a system of two equations with two incognito:<br />Defining this way: <br />Substituting in the system: <br />
7. 7. Having the coefficients as a result: <br />Finding the root, you to implement the conventional solution, but due to the error of rounding potential, an alternative formulation will be used:<br />Error<br />
8. 8. h = 0,1x2 = 5 x1 = 5,5 x0 =4,5<br />
9. 9. BIBLIOGRAGHY<br />http://lc.fie.umich.mx/~calderon/programacion/Mnumericos/Muller.html<br />http://aprendeenlinea.udea.edu.co/lms/moodle/mod/resource/view.php?id=24508<br />
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