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It's required to solve that equation: f(x) = x.^3 - 0.165*x.^2 + 3.993*10.^-4 using Newton-Raphson Method with initial guess (x0 = 0.05) to 3 iterations and also, plot that function.

Please help me with the code (i have MATLAB R2010a) ... I want the code to be with steps and iterations and if possible calculate the error also, please

Bruno Pop-Stefanov
on 25 Nov 2013

Edited: Brewster
on 25 Nov 2013

x = 0.05;

x_old = 100;

x_true = 0.0623776;

iter = 0;

while abs(x_old-x) > 10^-3 && x ~= 0

x_old = x;

x = x - (x^3 - 0.165*x^2 + 3.993*10^-4)/(3*x^2 - 0.33*x);

iter = iter + 1;

fprintf('Iteration %d: x=%.20f, err=%.20f\n', iter, x, x_true-x);

pause;

end

You can plot the function with, for example:

x = -10:0.01:10;

f = x.^3 - 0.165*x.^2 + 3.993*10^-4;

figure;

plot(f)

grid on

Bruno Pop-Stefanov
on 25 Nov 2013

Skyler Kolb
on 23 Sep 2015

if your initial guess is

x = 0.05

but then late declare your initial guess as a new value

x_old = x

in your while loop, how is that going to work? Won't that defeat the purpose of having an initial guess?

Pourya Alinezhad
on 25 Nov 2013

you can use the following line of code;

x = fzero(@(x)x.^3 - 0.165*x.^2 + 3.993*10.^-4,0.05)

Dhruv Bhavsar
on 28 Aug 2020

- Solve the system of non-linear equations.

x^2 + y^2 = 2z

x^2 + z^2 =1/3

x^2 + y^2 + z^2 = 1

using Newton’s method having tolerance = 10^(−5) and maximum iterations upto 20

%Function NewtonRaphson_nl() is given below.

fn = @(v) [v(1)^2+v(2)^2-2*v(3) ; v(1)^2+v(3)^2-(1/3);v(1)^2+v(2)^2+v(3)^2-1];

jacob_fn = @(v) [2*v(1) 2*v(2) -2 ; 2*v(1) 0 2*v(3) ; 2*v(1) 2*v(2) 2*v(3)];

error = 10^-5 ;

v = [1 ;1 ;0.1] ;

no_itr = 20 ;

[point,no_itr,error_out]=NewtonRaphson_nl(v,fn,jacob_fn,no_itr,error)

NewtonRaphson_nl_print(v,fn,jacob_fn,no_itr,error);

# OUTPUT.

Functions Below.

function [v1 , no_itr, norm1] = NewtonRaphson_nl(v,fn,jacob_fn,no_itr,error)

% nargin = no. of input arguments

if nargin <5 , no_itr = 20 ; end

if nargin <4 , error = 10^-5;no_itr = 20 ; end

if nargin <3 ,no_itr = 20;error = 10^-5; v = [1;1;1]; end

v1 = v;

fnv1 = feval(fn,v1);

i = 0;

while true

jacob_fnv1 = feval(jacob_fn,v1);

H = jacob_fnv1\fnv1;

v1 = v1 - H;

fnv1 = feval(fn,v1);

i = i + 1 ;

norm1 = norm(fnv1);

if i > no_itr && norm1 < error, break , end

%if norm(fnv1) < error , break , end

end

end

function [v1 , no_itr, norm1] = NewtonRaphson_nl_print(v,fn,jacob_fn,no_itr,error)

v1 = v;

fnv1 = feval(fn,v1);

i = 0;

fprintf(' Iteration| x | y | z | Error | \n')

while true

norm1 = norm(fnv1);

fprintf('%10d |%10.4f| %10.4f | %10.4f| %10.4d |\n',i,v1(1),v1(2),v1(3),norm1)

jacob_fnv1 = feval(jacob_fn,v1);

H = jacob_fnv1\fnv1;

v1 = v1 - H;

fnv1 = feval(fn,v1);

i = i + 1 ;

norm1 = norm(fnv1);

if i > no_itr && norm1 < error, break , end

%if norm(fnv1) < error , break , end

end

end

This covers answer to your question and also queries for some comments I read in this thread.

Juan Sebastian Castro Barrero
on 12 Feb 2021 at 16:04

i need make a program in matlab to solve

F(1)=1+(x(1)^2)-(x(2)^2)+((exp(x(1)))*cos(x(2)));

F(2)=(2*(x(1))*(x(2)))+((exp(x(1)))*sin(x(2)));

starting initials (-1,4)

5 iterations.

can you help me?

Eduardo
on 13 Apr 2014

Hello,

I am trying to make a program using the Newton-Raphson method for complex equations, but I am in a infinite loop.

If I change the expression,

x = x - (x^3 - 0.165*x^2 + 3.993*10^-4)/(3*x^2 - 0.33*x);

For this:

x = x - (sqrt(-x))/(-0.5.*(1./sqrt(-x)));

The algorithm does not work.

how can I use a complex equation in this case ??

Thank you very much.

Valdes Corleone
on 1 Sep 2018

Sayeed
on 21 Oct 2018

madhan ravi
on 21 Oct 2018

Please ask a separate question question because it would make this thread unrelated

Sayeed
on 21 Oct 2018

Thanks, I did. Can u help with that?

https://se.mathworks.com/matlabcentral/answers/425183-code-for-equation-with-ln

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