In numerical analysis , Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree. The algorithm first appeared in the appendix of the book Applied Aerodynamics by Leonard Bairstow. See root-finding algorithm for other algorithms. The roots of the quadratic may then be determined, and the polynomial may be divided by the quadratic to eliminate those roots. This process is then iterated until the polynomial becomes quadratic or linear, and all the roots have been determined.

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Bairstow Method is an iterative method used to find both the real and complex roots of a polynomial. It is based on the idea of synthetic division of the given polynomial by a quadratic function and can be used to find all the roots of a polynomial.

Given a polynomial say,. On solving we get Now proceeding in the above manner in about ten iteration we get with. Roots of are: Roots are i. Exercises: 1 Use initial approximation to find a quadratic factor of the form of the polynomial equation. It may be noted that is considered based on some guess values for.

So Bairstow's method reduces to determining the values of r and s such that is zero. For finding such values Bairstow's method uses a strategy similar to Newton Raphson's method. Since both and are functions of r and s we can have Taylor series expansion of , as:. To solve the system of equations , we need the partial derivatives of w. Bairstow has shown that these partial derivatives can be obtained by synthetic division of , which amounts to using the recurrence relation replacing with and with i.

If the quotient polynomial is a third or higher order polynomial then we can again apply the Bairstow's method to the quotient polynomial. The previous values of can serve as the starting guesses for this application. Now on using we get So at this point Quotient is a quadratic equation.

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## Bairstow’s Method

Bairstow Method is an iterative method used to find both the real and complex roots of a polynomial. It is based on the idea of synthetic division of the given polynomial by a quadratic function and can be used to find all the roots of a polynomial. Given a polynomial say,. On solving we get Now proceeding in the above manner in about ten iteration we get with. Roots of are: Roots are i.

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## Bairstow's method

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## Bairstow's Method

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