edit
I
??? Undefined function or variable 'I'.

A=rand(4);
[L,U]=lu(A);
L

L =

    0.8920   -0.3250    1.0000         0
    0.9917    1.0000         0         0
    0.1390   -0.4552    0.2567    1.0000
    1.0000         0         0         0

L*U

ans =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419

A

A =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419

[L,U,P]=lu(A);
L

L =

    1.0000         0         0         0
    0.9917    1.0000         0         0
    0.8920   -0.3250    1.0000         0
    0.1390   -0.4552    0.2567    1.0000

U

U =

    0.9134    0.5469    0.9706    0.1419
         0   -0.4448    0.0024    0.3447
         0         0    0.0925    0.9426
         0         0         0    0.6955

L*U

ans =

    0.9134    0.5469    0.9706    0.1419
    0.9058    0.0975    0.9649    0.4854
    0.8147    0.6324    0.9575    0.9572
    0.1270    0.2785    0.1576    0.8003

P*A

ans =

    0.9134    0.5469    0.9706    0.1419
    0.9058    0.0975    0.9649    0.4854
    0.8147    0.6324    0.9575    0.9572
    0.1270    0.2785    0.1576    0.8003

% A*x=b
% L*U = P*A
% P*A*x=P*b
% L*U*x=P*b
% U*x=y
% L*y=P*b
A=toeplitz([-2,1,0,0,0]);
b=ones(5,1);
y0=[1,2,3,4,5]';
y=thetametodolin(A,b,y0,1,1/2,10);
y

y =

  Columns 1 through 4

    1.0000    1.0954    1.1826    1.2627
    2.0000    2.0997    2.1984    2.2951
    3.0000    3.0988    3.1936    3.2818
    4.0000    4.0749    4.1079    4.1132
    5.0000    4.5489    4.1846    3.8884

  Columns 5 through 8

    1.3369    1.4060    1.4706    1.5310
    2.3889    2.4791    2.5653    2.6470
    3.3623    3.4349    3.4999    3.5579
    4.1007    4.0774    4.0478    4.0154
    3.6457    3.4455    3.2793    3.1405

  Columns 9 through 11

    1.5877    1.6409    1.6908
    2.7242    2.7968    2.8648
    3.6096    3.6557    3.6970
    3.9822    3.9497    3.9189
    3.0239    2.9255    2.8422

y=thetametodolin(A,b,y0,1,1/2,20);
y(:,21)

ans =

    1.6907
    2.8648
    3.6966
    3.9187
    2.8436

y=thetametodolin(A,b,y0,1,1/2,40);
y(:,41)

ans =

    1.6907
    2.8647
    3.6965
    3.9186
    2.8440

y=thetametodolin(A,b,y0,1,1,40);
y(:,41)

ans =

    1.6868
    2.8593
    3.6913
    3.9211
    2.8595

y=thetametodolin(A,b,y0,1,1,160);
y(:,161)

ans =

    1.6897
    2.8633
    3.6951
    3.9192
    2.8480

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica

ans =

   3.1172e-05


ans =

   4.8464e-11


ans =

   5.5373e-17


ans =

   3.0786e-05


ans =

   4.7155e-11


ans =

   3.7975e-17


ans =

   3.0106e-05


ans =

   4.4983e-11


ans =

   1.3775e-17


ans =

   2.9154e-05


ans =

   4.2081e-11


ans =

   3.4356e-17


ans =

   2.7961e-05


ans =

   3.8618e-11


ans =

   1.0282e-17


ans =

   2.6565e-05


ans =

   3.4779e-11


ans =

   3.0777e-17


ans =

   2.5008e-05


ans =

   3.0753e-11


ans =

   2.3885e-17

??? Operation terminated by user during ==>
<a href="matlab: opentoline('/home/accounts/personale/clrmrc90/aa1213/equazioni_differenziali/logistica.m',25,0)">logistica at 25</a>

% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica

ans =

   3.1198e-05


ans =

   2.5907e-08


ans =

   2.1526e-11


ans =

   1.7834e-14

??? Operation terminated by user during ==>
<a href="matlab: opentoline('/home/accounts/personale/clrmrc90/aa1213/equazioni_differenziali/logistica.m',25,0)">logistica at 25</a>

% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

logistica
diary off