Bairstow,s Method
المؤلف:
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T
المصدر:
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press
الجزء والصفحة:
pp. 277 and 283-284
9-12-2021
1039
Bairstow's Method
A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial 
with real coefficients.
![[x-(a+ib)][x-(a-ib)]=x^2+2ax+(a^2+b^2)=x^2+Bx+C.](https://mathworld.wolfram.com/images/equations/BairstowsMethod/NumberedEquation1.gif) |
(1)
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Now write the original polynomial as
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(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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(8)
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Now use the two-dimensional Newton's method to find the simultaneous solutions.
REFERENCES:
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 277 and 283-284, 1989.
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