CALCULATION OF MULTIPLE ROOTS AND COMPLEX ROOTS

CALCULATION OF MULTIPLE ROOTS AND COMPLEX ROOTS

When there are complex roots closed methods can not be used as the criterion for defining the range is the sign change does not apply to complex values.

For this reason, special methods have been developed to find real and complex roots of polynomials.

• MULLER'S METHOD
• THE BAIRSTOW METHOD

*MULLER METHOD:

The secant method obtains an approximation of the root leading a straight line to the axis X with two values of the function. Muller's method is similar, but building a parabola with three points.

The method consists of obtaining the coefficients of the parabola through the three points. These coefficients are used in the quadratic formula to get the value where the parabola intersects the X axis, ie the estimated result.

Once you know the approximate coefficients found through the root of the quadratic equation where:



Having to solve the quadratic to find the new result leaves open the possibility that complex roots can be calculated, where i = root of -1.

As a general rule is to choose the root whose discriminant D1 or D2
is the largest since this ensures that the new root is closest to the initial values proposed










*Bairstow Method

NUMERICAL METHODS

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REFERENCES:

(1)NUMERICAL METHODS FOR ENGINEERS WITH PERSONAL COMPUTER APPLICATIONS. STEVEN C. Chapra / Raymond P. CANALE

(2)http://www.concepcionabraira.info/wp/?p=305

(3) internet-google.

(4)Enciclopedia libre wikipedia