R: Laguerre's Method

laguerre {pracma} | R Documentation

## 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.

### Details

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

### Value

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

### Note

Computations are caried out in complex arithmetic, and it is possible to obtain a complex root even if the starting estimate is real.

### 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))

[Package pracma version 2.0.4 Index]