## Newton's Method

Content: This page contains an applet illustrating Newton's method and instructions for its use.

Applet

Theory

Analysis for Computer Scientists, Chapter 8

Help

### Entering the function

To visualise Newton's method a function must be defined in the field f(x)= (detailed information on the syntax can be found here). In the field Interval an interval must be specified in which the function has a zero. If the button Draw is pressed, the graph is displayed and the starting value of the iteration is visualised. The starting value can be changed by drag-and-drop (i.e. by pressing the left mouse button and moving the mouse along the x-axis).

### Visualisation of Newton's method

The desired accuracy can be entered in the field Accuracy. Furthermore, with the options Standard method or Simplified method it can be specified whether the Jacobian of f is computed in every step or just once at the beginning of the iteration. Pressing the button Newton visualises the method step by step. The current approximation xn to the zero, the defect |f(xn)| and the increment |xn-xn-1| are listed in the table below the graph. The iteration is stopped when the desired accuracy is achieved. By pressing the button Draw the iteration is reset and can be started again (e.g., with another starting value).

### Questions

If you have further questions or comments, or if you found a bug, please send us an e-mail.

Financially supported by

University of Innsbruck: New Media and Learning Technologies
Austrian Federal Ministry of Education, Science and Research

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