# newtonRaphson: Rootfinding through Newton-Raphson or Secant. In pracma: Practical Numerical Math Functions

## Description

Finding roots of univariate functions. (Newton never invented or used this method; it should be called more appropriately Simpson's method!)

## Usage

 ```1 2``` ```newtonRaphson(fun, x0, dfun = NULL, maxiter = 500, tol = 1e-08, ...) newton(fun, x0, dfun = NULL, maxiter = 500, tol = 1e-08, ...) ```

## Arguments

 `fun` Function or its name as a string. `x0` starting value for newtonRaphson(). `dfun` A function to compute the derivative of `f`. If `NULL`, a numeric derivative will be computed. `maxiter` maximum number of iterations; default 100. `tol` absolute tolerance; default `eps^(1/2)` `...` Additional arguments to be passed to f.

## Details

Well known root finding algorithms for real, univariate, continuous functions.

## Value

Return a list with components `root`, `f.root`, the function value at the found root, `iter`, the number of iterations done, and `root`, and the estimated precision `estim.prec`

The estimated precision is given as the difference to the last solution before stop; this may be misleading.

## References

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

`newtonHorner`

## Examples

 ```1 2 3 4``` ```# Legendre polynomial of degree 5 lp5 <- c(63, 0, -70, 0, 15, 0)/8 f <- function(x) polyval(lp5, x) newton(f, 1.0) # 0.9061798459 correct to 10 decimals in 5 iterations ```

### Example output

```\$root
[1] 0.9061798

\$f.root
[1] 6.661338e-16

\$niter
[1] 6

\$estim.prec
[1] 6.78706e-16
```

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