pracma (version 1.9.9)

laguerre: Laguerre's Method

Description

Laguerre's method for finding roots of complex polynomials.

Usage

laguerre(p, x0, nmax = 25, tol = .Machine$double.eps^(1/2))

Arguments

p

real or complex vector representing a polynomial.

x0

real or complex point near the root.

nmax

maximum number of iterations.

tol

absolute tolerance.

Value

The root found, or a warning about the number of iterations.

Details

Uses values of the polynomial and its first and second derivative.

References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

See Also

roots

Examples

# 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))