Laguerre's Method
Laguerre's method for finding roots of complex polynomials.
laguerre(p, x0, nmax = 25, tol = .Machine$double.eps^(1/2))
p |
real or complex vector representing a polynomial. |
x0 |
real or complex point near the root. |
nmax |
maximum number of iterations. |
tol |
absolute tolerance. |
Uses values of the polynomial and its first and second derivative.
The root found, or a warning about the number of iterations.
Computations are caried out in complex arithmetic, and it is possible to obtain a complex root even if the starting estimate is real.
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.
# 1 x^5 - 5.4 x^4 + 14.45 x^3 - 32.292 x^2 + 47.25 x - 26.46 p <- c(1.0, -5.4, 14.45, -32.292, 47.25, -26.46) laguerre(p, 1) #=> 1.2 laguerre(p, 2) #=> 2.099987 (should be 2.1) laguerre(p, 2i) #=> 0+2.236068i (+- 2.2361i, i.e sqrt(-5))
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