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The Quarterly Journal of Mechanics and Applied Mathematics 1959 12(3):365-378; doi:10.1093/qjmam/12.3.365
© 1959 by Oxford University Press
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ROUTH TEST FUNCTION METHODS FOR THE NUMERICAL SOLUTION OF POLYNOMIAL EQUATIONS

C. MACK

( (British Cotton Industry Research Association, Manchester, 20) )

In this paper two iterative methods are developed for the numerical solution of polynomial equations with real coefficients. The first (the x) method is based upon a systematic application of Routh's test (1) for the number of zeros of a polynomial with positive real parts. The second (the a) method uses the teat in a different manner to evaluate quadratic factors directly. The methods have certain desirable features: (i) they always converge, even from an arbitrary start, (ii) numerical checks can be used at each stage, and (iii) with modern fully automatic desk machines with retaining keys they are relatively quick. Some properties of Routh's test are proved and an algebraic proof of the test itself (and two proofs of the fundamental theorem of algebra) are also given.


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