Question:A List of Lists...

Question:A List of Lists...

Maple 11

Useing the following procedure I'd like to collect a set of  roots in a list of lists, so they can be manipulated and presented in various plot options. Some of which could be very interesting (to me only perhaps).

One option is to create a loop which produces values of newton roots x0 for a given function. For example:              f:=x->(x^7)-5

for x from -1 to 1 by 0.05 do

u:= [newton(f,x*I-I,20,0.01)]:

print (u);

end do:

This produces many values...but I have no idea how to remove the warning that the iteration has failed or how to place them in a list of which I described. I think it would be of the form [[x1+iy1],...[xN+iyN]]. I am at some what of a loss! Any help would be greatfully recieved!!!

> newton := proc( f, # the function x0, # the initial guess n, # step count limit tol # error tolerance)

local x, g, k;

g := D(f); # the derivative f’(x)

x[0] := evalf(x0); # initialize the iteration

for k from 1 to n do # loop for newton’s iteration

# Newton’s iteration formula

x[k] := evalf( x[k-1] - f(x[k-1])/g(x[k-1]) );

# exit early if possible, with luck

if abs(x[k]-x[k-1]) < tol then

return x[k];

end if;

end do;

return "Newton’s iteration fails"

end proc:

﻿