using last result to start an iteration process and continously

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bayoishola20 2015-2-17

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评论： Guillaume 2015-2-19

Please how do I make an answer gotten to repeat a process of two variables and then until its convergence. In other words, I don't know the number of iterations to be done.

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Answer 1

Guillaume 2015-2-17

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I'm sorry to say that your question is not clear at all. It's obvious that English is not your native language.

Anyway, to have a loop that terminates under a given condition, use while:

condition = false;
while ~condition
   condition = resultofsomeoperation();
end

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bayoishola20 2015-2-18

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Sorry about the unclear question,

clear all   % Clear variable cache;workspace
clc         % Clear screen;command window
% Initial x1 and x2
x1 = 5, x2 = 4
% Equations
y1 = (x1-3)^2 + (2*x2 - 8)^2
y2 =(x1-4)^2 + (x2 - 10)^2
%Given y values
y = [5;49]
% First set of y values
yo = [y1;y2]
f = y - yo
syms xo1 xo2 % xo1,xo2 are symbols
A11 = diff((x1-3)^2 + (2*x2 - 8)^2,x1) %differentiation wrt "xo1"
A12 =diff((x1-3)^2 + (2*x2 - 8)^2,x2)  %differentiation wrt "xo2"
A21 =diff((x1-4)^2 + (x2 - 10)^2,x1)   %differentiation wrt "xo1"
A22 =diff((x1-4)^2 + (x2 - 10)^2,x2)   %differentiation wrt "xo2"
A = [A11 A12;A21 A22]
% Initial x1 and x2
for i = 5
    x1 = 5, x2 = 4
A = [ 2*x1 - 6, 8*x2 - 32; 2*x1 - 8, 2*x2 - 20]
dx = inv(A'*A)*(A'*f)
dx1 = dx(1,1)
dx2 = dx(2,1)
[dx1;dx2]
new_x1_x2 = [x1+dx1; x2+dx2]
end

I need the values of x1 and x2 to be repeated so that at the end of the day, it does converge. More like the newton raphson, Runge-Kutta and co. iterations.

Guillaume 2015-2-19

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Like I said, use a while:

%initialise data
%... calculate A, f, etc.
x1 = 5, x2 = 4;
convergencethreshold = 1e-8; %or whatever you want
dx = [Inf Inf];
while any(abs(dx) > convergencethreshold)
   A = [2*x1 - 6, 8*x2 - 32; 2*x1 - 8, 2*x2 - 20]
   dx = inv(A'*A)*(A'*f)
   x1 = x1 + dx;
   x2 = x2 + dx;
end