Description Usage Arguments Value Author(s) References Examples

Finds roots of univariate functions by modifying the usual Newton-Raphson method by decreasing the step sizes when necessary.

1 | ```
damped.newton(fun, derf, x0, eps, maxit = 20, damp = seq(0, 40),silent=TRUE)
``` |

`fun` |
a function for which the root is searched. |

`derf` |
a function which is the first derivative of the function to be solved. |

`x0` |
a numeric value to be used to start the algorithm. |

`eps` |
a numeric value to be considered as the tolerance for convergence of the algorithm. |

`maxit` |
a numeric value which denotes maximum number of iterations to be consumed. |

`damp` |
a vector beginning from zero and increasing by one unit to decrease the step sizes. |

`silent` |
a logical statement which decides whether the iterations should be printed. |

Returns a numeric result of the root.

Ozgur Asar, Ozlem Ilk

Bose, K. S. (2008). *Numeric Computing in Fortran*. Alpha Science.

Conte, S. D., de Boor, C. (1980). *Elementary Numerical Analysis: An Algorithmic Approach, third edition*. New York: McGraw-Hill Publications.

Ilk, O. (2011). *R Yazilimina Giris* [Introduction to R Language]. ODTU Yayincilik [METU Press].

1 2 3 |

```
Iteration: 1 ; Result= 1.318883
Iteration: 2 ; Result= 0.8868571
Iteration: 3 ; Result= 0.6656977
Iteration: 4 ; Result= 0.6085951
Iteration: 5 ; Result= 0.6054324
Iteration: 6 ; Result= 0.6054234
Solution: 0.6054234
[1] 0.6054234
```

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