Description Usage Arguments Details Value Note Author(s) References See Also

View source: R/newton.method.R

This function provides an illustration of the iterations in Newton's method.

1 2 3 4 5 6 7 8 9 10 11 12 |

`FUN` |
the function in the equation to solve (univariate), which has to be defined without braces like the default one (otherwise the derivative cannot be computed) |

`init` |
the starting point |

`rg` |
the range for plotting the curve |

`tol` |
the desired accuracy (convergence tolerance) |

`interact` |
logical; whether choose the starting point by cliking on the curve (for 1 time) directly? |

`col.lp` |
a vector of length 3 specifying the colors of: vertical lines, tangent lines and points |

`main, xlab, ylab` |
titles of the plot; there are default values for them
(depending on the form of the function |

`...` |
other arguments passed to |

Newton's method (also known as the Newton-Raphson method or the Newton-Fourier method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function f(x).

The iteration goes on in this way:

*x[k + 1] = x[k] -
FUN(x[k]) / FUN'(x[k])*

From the starting value *x_0*, vertical lines and points are plotted to
show the location of the sequence of iteration values *x1, x2, …*; tangent lines are drawn to illustrate the
relationship between successive iterations; the iteration values are in the
right margin of the plot.

A list containing

`root ` |
the root found by the algorithm |

`value ` |
the value of |

`iter` |
number of
iterations; if it is equal to |

The algorithm might not converge – it depends on the starting value. See the examples below.

Yihui Xie

Examples at https://yihui.org/animation/example/newton-method/

For more information about Newton's method, please see https://en.wikipedia.org/wiki/Newton's_method

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