Thread Subject:

Matlab question for Newton Raphson

Need to do 5 iterations...for this problem not including 0 which is 1 and 0

f1(x1, x2) = 10x1sinx2 + 2 = 0
f2(x1, x2) = 10x1^2? 10x1cos x2 + 1 = 0

where x0 = [ 1 ; 0]

x01 = 1
x02 = 0


Please need the code plus the first five iterations for x1 and x2.....ive been trying but...keep getting errors..and its due tomorrow lol :( at 5:30 latest

"Carlos Mallqui" wrote in message <jnaeda$p5b$1@newscl01ah.mathworks.com>...
> Need to do 5 iterations...for this problem not including 0 which is 1 and 0
>
> f1(x1, x2) = 10x1sinx2 + 2 = 0
> f2(x1, x2) = 10x1^2? 10x1cos x2 + 1 = 0
>
> where x0 = [ 1 ; 0]
>
> x01 = 1
> x02 = 0
>
>
> Please need the code plus the first five iterations for x1 and x2.....ive been trying but...keep getting errors..and its due tomorrow lol :( at 5:30 latest

Please post your code so we can comment on it.

James Tursa

maxiter = 5;
tol=1e-6
x=[1 0]%initial extimates
f=(10*x(1)*sin(x(2)))+2;%function
fx1=10*sin(x(2));%derivative of function w.r.t x1
fx2=10*x1*cos(x(2));%derivative of function w.r.t x2
J=[fx1 fx2] %Jacobian matrix of function
xold = x(:);
xnew = xold - J\f
for k=1:maxiter
xold = xnew;
niter = k;
xnew = xold - J\f;
if abs(xold-xnew)/abs(xnew) < tol
(niter == maxiter)
break
end
end
r = xnew

like this try for the next function also

"prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnaip9$c68$1@newscl01ah.mathworks.com>...
>
> f=(10*x(1)*sin(x(2)))+2;%function
> fx1=10*sin(x(2));%derivative of function w.r.t x1
> fx2=10*x1*cos(x(2));%derivative of function w.r.t x2


This should be

 fx2=10*x(1)*cos(x(2));

Once I make this change, your code runs without errors.

However, the code you've written attempts to solve the single equation in 2 unknowns,

(10*x(1)*sin(x(2)))+2=0

which of course could have infinite solutions. Are you sure that's what you're meant to do? It's more likely that you were meant to solve the following 2 equations simultaneously, i.e., as a system of 2 equations in 2 unknowns

f1(x1, x2) = 10x1sinx2 + 2 = 0
f2(x1, x2) = 10x1^2? 10x1cos x2 + 1 = 0

Doing so would make the solution more uniquely defined.

"prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnaip9$c68$1@newscl01ah.mathworks.com>...
> maxiter = 5;
> tol=1e-6
> x=[1 0]%initial extimates
> f=(10*x(1)*sin(x(2)))+2;%function
> fx1=10*sin(x(2));%derivative of function w.r.t x1
> fx2=10*x1*cos(x(2));%derivative of function w.r.t x2
> J=[fx1 fx2] %Jacobian matrix of function
> xold = x(:);
> xnew = xold - J\f
> for k=1:maxiter
> xold = xnew;
> niter = k;
> xnew = xold - J\f;
> if abs(xold-xnew)/abs(xnew) < tol
> (niter == maxiter)
> break
> end
> end
> r = xnew
====================


Another question you should be asking yourself is whether the Jacobian J is supposed to stay constant throughout your iterations 1:maxiter. If so, what you've implemented is called the secant method, not Newton-Raphson.

"Matt J" wrote in message <jnb0hj$4ap$1@newscl01ah.mathworks.com>...
> "prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnaip9$c68$1@newscl01ah.mathworks.com>...
> > maxiter = 5;
> > tol=1e-6
> > x=[1 0]%initial extimates
> > f=(10*x(1)*sin(x(2)))+2;%function
> > fx1=10*sin(x(2));%derivative of function w.r.t x1
> > fx2=10*x1*cos(x(2));%derivative of function w.r.t x2
> > J=[fx1 fx2] %Jacobian matrix of function
> > xold = x(:);
> > xnew = xold - J\f
> > for k=1:maxiter
> > xold = xnew;
> > niter = k;
> > xnew = xold - J\f;
> > if abs(xold-xnew)/abs(xnew) < tol
> > (niter == maxiter)
> > break
> > end
> > end
> > r = xnew
> ====================
>
>
> Another question you should be asking yourself is whether the Jacobian J is supposed to stay constant throughout your iterations 1:maxiter. If so, what you've implemented is called the secant method, not Newton-Raphson.


Yes Matt, you are right i tried to solve 2 equation with 2 unknowns only, since i am a beginner, i saw this question and tried myself doing newton raphson. and thank you very much for your correction, i had learned few things form it, and the Jacobian should change its value on each iteration, it should not have same value,.

may i know what change i should do to make it Newton raphson method

maxiter = 5;
tol=1e-6
x=[1 0]%initial extimates
xold = x(:);
for k=1:maxiter
% xold = xnew;
    f1=(10*x(1)*sin(x(2)))+2;%function
    f2=10*x(1)*cos(x(2))+1;%function
    f1x1=10*sin(x(2));%derivative of function w.r.t x1
    f1x2=10*x(1)*cos(x(2));%derivative of function w.r.t x2
    f2x1=10*cos(x(2));
    f2x2=-10*x(1)*sin(x(2));
    f=[f1 f2]'
    J =[f1x1 f1x2; f2x1 f2x2] %Jacobian matrix of function
    xnew = xold - J\f;
    x=xnew
    if abs(xold-xnew)/abs(xnew) < tol
        r=xnew
        break
    end
end

i tried to solve with one equation itself. after reading your comment only i came to know my blunt. now i tried 2 equation with 2 unknowns, and the value of J is changing in each iterations. am i right now ??

"Matt J" wrote in message <jnb0hj$4ap$1@newscl01ah.mathworks.com>...
> "prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnaip9$c68$1@newscl01ah.mathworks.com>...
> > maxiter = 5;
> > tol=1e-6
> > x=[1 0]%initial extimates
> > f=(10*x(1)*sin(x(2)))+2;%function
> > fx1=10*sin(x(2));%derivative of function w.r.t x1
> > fx2=10*x1*cos(x(2));%derivative of function w.r.t x2
> > J=[fx1 fx2] %Jacobian matrix of function
> > xold = x(:);
> > xnew = xold - J\f
> > for k=1:maxiter
> > xold = xnew;
> > niter = k;
> > xnew = xold - J\f;
> > if abs(xold-xnew)/abs(xnew) < tol
> > (niter == maxiter)
> > break
> > end
> > end
> > r = xnew
> ====================
>
>
> Another question you should be asking yourself is whether the Jacobian J is supposed to stay constant throughout your iterations 1:maxiter. If so, what you've implemented is called the secant method, not Newton-Raphson.



thanks but...which one should i try inputting into Matlab...im guessing Matts'....also...the questions is use Newtons Raphsons method and solve x1 and x2 5 iterations...nothing else aside of that...o well and the given initial conditions

"prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnb5f4$m28$1@newscl01ah.mathworks.com>...
> maxiter = 5;
> tol=1e-6
> x=[1 0]%initial extimates
> xold = x(:);
> for k=1:maxiter
> % xold = xnew;
> f1=(10*x(1)*sin(x(2)))+2;%function
> f2=10*x(1)*cos(x(2))+1;%function
> f1x1=10*sin(x(2));%derivative of function w.r.t x1
> f1x2=10*x(1)*cos(x(2));%derivative of function w.r.t x2
> f2x1=10*cos(x(2));
> f2x2=-10*x(1)*sin(x(2));
> f=[f1 f2]'
> J =[f1x1 f1x2; f2x1 f2x2] %Jacobian matrix of function
> xnew = xold - J\f;
> x=xnew
> if abs(xold-xnew)/abs(xnew) < tol
> r=xnew
> break
> end
> end
>
> i tried to solve with one equation itself. after reading your comment only i came to know my blunt. now i tried 2 equation with 2 unknowns, and the value of J is changing in each iterations. am i right now ??



>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

this is...the example the professor posted...for a similar problem...with some code...maybe it will help answer matts question...whethere he wants them together or not.....

clear, clc
x = [1;1]; % initial conditions
nit=10; % number of iterations
for i=1:nit
f(:,i) = [x(1,i)*x(1,i)-x(2,i)-1; x(2,i)*x(2,i)-x(1,i)-1];
delta = 4*x(1,i)*x(2,i)-1;
Jinv = (1/delta)*[ 2*x(2,i) 1; 1 2*x(1,i)];
dx(:,i) = -Jinv*f(:,i);
x(:,i+1) = x(:,i) + dx(:,i);
end
numofit = (0:nit);
output = [numofit; x];
fprintf(’\n nofit \t x(1) \t x(2) \n’);
fprintf(’-------------------------------\n’);
fprintf(’%7.0f \t %7.4f \t %7.4f\n’,output);


Use the Newton-Raphson method to solve
f1(x1, x2) = x1^2? x2 ? 1 = 0
f2(x1, x2) = x2^2? x1 ? 1 = 0

intial conditions are both 1

in the solution the find the J marix....as well Delta...etc

but this is the code for the iterations where nit is number of iterations...

please help moi..thanks :D

"prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnb5f4$m28$1@newscl01ah.mathworks.com>...
>
> i tried to solve with one equation itself. after reading your comment only i came to know my blunt. now i tried 2 equation with 2 unknowns, and the value of J is changing in each iterations. am i right now ??
==============

I think you're computing J correctly, but now xold is not getting updated with every iteration.

You should be able to check whether everything is working by running with large maxiter and seeing if it converges to a solution.

"Matt J" wrote in message <jnbijm$fde$1@newscl01ah.mathworks.com>...
> "prabhakaran m" <prabha.gahon@gmail.com> wrote in message <jnb5f4$m28$1@newscl01ah.mathworks.com>...
> >
> > i tried to solve with one equation itself. after reading your comment only i came to know my blunt. now i tried 2 equation with 2 unknowns, and the value of J is changing in each iterations. am i right now ??
> ==============
>
> I think you're computing J correctly, but now xold is not getting updated with every iteration.
>
> You should be able to check whether everything is working by running with large maxiter and seeing if it converges to a solution.


>>>>>>>

is it updating fine up to a certain iteration?....

"Carlos Mallqui" wrote in message <jnbjh8$jkn$1@newscl01ah.mathworks.com>...
>
>
> is it updating fine up to a certain iteration?....

You tell me.

"Matt J" wrote in message <jnbomh$dv1$1@newscl01ah.mathworks.com>...
> "Carlos Mallqui" wrote in message <jnbjh8$jkn$1@newscl01ah.mathworks.com>...
> >
> >
> > is it updating fine up to a certain iteration?....
>
> You tell me.


>>>>>


x =

   -0.1000
   -0.2000

x =

    1.0417
    2.1588

x =

   -0.1527
    0.1864

x =

    1.0173
    1.1660

x =

   -0.2406
    0.0129

im thinking it updates for....the 2nd and 4th iteration..the other numbers...that it spits out are just...odd :S

"Carlos Mallqui" wrote in message <jnbv2f$cn7$1@newscl01ah.mathworks.com>...
>
> x =
>
> -0.1000
> -0.2000
>
> x =
>
> 1.0417
> 2.1588
>
> x =
>
> -0.1527
> 0.1864
>
> x =
>
> 1.0173
> 1.1660
>
> x =
>
> -0.2406
> 0.0129
>
> im thinking it updates for....the 2nd and 4th iteration..the other numbers...that it spits out are just...odd :S
===========

Here you're displaying the progress of the variable x.
I asked you to check the progress of xold.

You will see that it is not changing at all throughout the iterations, because there is no statement in the for-loop that updates it.

"Matt J" wrote in message <jnc0bn$hvp$1@newscl01ah.mathworks.com>...
> "Carlos Mallqui" wrote in message <jnbv2f$cn7$1@newscl01ah.mathworks.com>...
> >
> > x =
> >
> > -0.1000
> > -0.2000
> >
> > x =
> >
> > 1.0417
> > 2.1588
> >
> > x =
> >
> > -0.1527
> > 0.1864
> >
> > x =
> >
> > 1.0173
> > 1.1660
> >
> > x =
> >
> > -0.2406
> > 0.0129
> >
> > im thinking it updates for....the 2nd and 4th iteration..the other numbers...that it spits out are just...odd :S
> ===========
>
> Here you're displaying the progress of the variable x.
> I asked you to check the progress of xold.
>
> You will see that it is not changing at all throughout the iterations, because there is no statement in the for-loop that updates it.


>>>>>>

Matlab and me dont go along lol...ill have to learn at some other time i have this due in like few hours hours..ill have to make up something and go for part marks...if i at least had the values for 5 iterations for x1 and x2 would be great...if not thanks for taking time in replying..Both