# laguerre: Laguerre's Method In pracma: Practical Numerical Math Functions

## Description

Laguerre's method for finding roots of complex polynomials.

## Usage

 `1` ```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.

`roots`

## Examples

 ```1 2 3 4 5``` ```# 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)) ```

### Example output

```[1] 1.2
[1] 2.099987
[1] 0+2.236068i
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.