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GeoGebra: Fixed Point Iteration: Rearrangement Method x=g(x)

October 29th, 2013 Leave a comment Go to comments

Numerical method for finding roots of f(x) = 0, by rearranging to x = g(x) and iterating
xn+1 = g(xn)

Click the image to link to GeoGebraTube

Designed principally for use with the MEI-OCR C3 Coursework on Numerical Methods

  1. Saf
    June 7th, 2014 at 11:46 | #1

    Hi Micky
    Any chance you can send me some info on how you made this and the other ggb for MEI cw?

    • Micky
      June 7th, 2014 at 15:24 | #2

      Hello Saf, probably the best thing you can do is download the ggb files and try to deconstruct them. Having said that, I just tried to do that myself, because it’s a year since I made these and I’ve largely forgotten how I managed it. Most of the interesting stuff is in the spreadsheet module – have a look in there. To get the iteration results to display on the screen, well that was a real challenge: All the text lines’ positions are dependent on the position of a single hidden point, the position of which is determined by formulas in terms of zoomX, zoomY, posX and posY. Additionally, the gap between each text line is dependent on zoomY and the gap between the two columns of text is dependent on zoomX. Bloody complicated! It would be useful if you could specify an object’s position relative to the window, rather than the axes – that would make such things a lot easier.

      My school uses Autograph, which I very much dislike, so I made these which are far easier to interact with. I give the students a link to the applets on GeoGebraTube and they play around with them to get a feel for each numerical method. It’s way too complicated for them to try to build themselves. They use Excel to do the requisite mathematics for the coursework, and they are allowed to put screenshots of these applets in their submission.

      Change of sign is dead easy – just use Excel.

      Best wishes