%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%STUDENTS OF 412 ARE ENTITLED TO USE A VARIATION OF THIS FILE FOR
%THEIR ASSIGNMENT.  IF YOU DO THAT, REPORT THAT FACT ON THE 
%ASSIGNMENT (WRITE : `I USED THE CODE AT CLASS ACCOUNT AS MY BASE CODE')
%YOU MAY WISH, HOWEVER, TO WRITE SOMETHING A BIT MORE SOPHISTICATED
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%in this file, we try to solve the equation x^3=sin(x)
%using four different fixed point algorithms. 
%rat is the (estimated) ratio between the current error and the previous one. 
%only one iteration is performed. 
%before you use this file, type `n=1'. This will initialize the
%parameters in the code, and will also keep a counter on the number
%of iterations.  the value of rat after one iteration is meaningless.
%note that the solution is around .9

n=1

n =

     1

fixed_point

rat =

   -0.0559   -0.1585   -0.1585   -0.0645


x =

    0.9441    0.8415    0.8415    0.9355

fixed_point

rat =

    0.2134   -1.3345   -0.9449    0.0878


x =

    0.9322    1.0530    0.9913    0.9299

fixed_point

rat =

    0.2275   -1.2735   -0.9167    0.1811


x =

    0.9294    0.7836    0.8540    0.9289

fixed_point

rat =

    0.2306   -1.3580   -0.9551    0.1898


x =

    0.9288    1.1495    0.9851    0.9287

fixed_point

rat =

    0.2313   -1.2541   -0.9351    0.1914


x =

    0.9287    0.6906    0.8625    0.9286

fixed_point

rat =

    0.2315   -1.4055   -0.9614    0.1917


x =

    0.9286    1.3356    0.9804    0.9286

fixed_point

rat =

    0.2315   -1.2255   -0.9462    0.1917


x =

    0.9286    0.5452    0.8688    0.9286

fixed_point

rat =

    0.2315   -1.5177   -0.9659    0.1917


x =

    0.9286    1.7447    0.9766    0.9286

fixed_point

rat =

    0.2315   -1.1848   -0.9536    0.1917


x =

    0.9286    0.3236    0.8738    0.9286

fixed_point

rat =

    0.2315   -1.9093   -0.9691    0.1917


x =

    0.9286    3.0370    0.9734    0.9286

fixed_point

rat =

    0.2315   -1.1151   -0.9589    0.1917


x =

    0.9286    0.0113    0.8779    0.9286

formatlong
??? Undefined function or variable 'formatlong'.

format long
fixed_point

rat =

   0.23151341695496 -29.18636973947528  -0.97167580046495   0.19172756220239


x =

   0.92862631028634  88.31909972374159   0.97069299656834   0.92862630881575

fixed_point

rat =

   0.23151341189675  -1.00012771055615  -0.96295031931709   0.19172746264867


x =

   0.92862630909165   0.00004450190562   0.88133974318030   0.92862630874784

fixed_point

rat =

   1.0e+02 *

   0.00231513453551  -2.54429213859449  -0.00973692285536   0.00191727252069


x =

   1.0e+04 *

   0.00009286263088   2.24709478334029   0.00009683423167   0.00009286263087

exit