The roots of an equation
(1) |
To find the th roots of a Complex Number, solve the equation . Then
(2) |
(3) |
(4) |
See also Bailey's Method, Bisection Procedure, Brent's Method, Crout's Method, Descartes' Sign Rule, False Position Method, Fundamental Theorem of Symmetric Functions, Graeffe's Method, Halley's Irrational Formula, Halley's Method, Halley's Rational Formula, Horner's Method, Householder's Method, Hutton's Method, Isograph, Jenkins-Traub Method, Laguerre's Method, Lambert's Method, Lehmer-Schur Method, Lin's Method, Maehly's Procedure, Muller's Method, Newton's Method, Polynomial, Ridders' Method, Root Dragging Theorem, Schröder's Method, Secant Method, Sturm Function, Sturm Theorem, Tangent Hyperbolas Method, Weierstraß Approximation Theorem
References
Arfken, G. ``Appendix 1: Real Zeros of a Function.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 963-967, 1985.
Boyer, C. B. A History of Mathematics. New York: Wiley, 1968.
Householder, A. S. The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Roots of Polynomials.'' §9.5 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 362-372, 1992.
© 1996-9 Eric W. Weisstein