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Gauss-Seidel method
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% GAUSS-SEIDEL ITERATIVE TECHNIQUE ALGORITHM 7.2
%
% To solve Ax = b given an initial approximation x(0).
%
% INPUT: the number of equations and unknowns n; the entries
% A(I,J), 1<=I, J<=n, of the matrix A; the entries
% B(I), 1<=I<=n, of the inhomogeneous term b; the
% entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
% maximum number of iterations N.
%
% OUTPUT: the approximate solution X(1),...,X(n) or a message
% that the number of iterations was exceeded.
syms('AA', 'OK', 'NAME', 'INP', 'N', 'I', 'J', 'A', 'X1');
syms('TOL', 'NN', 'K', 'ERR', 'S', 'FLAG', 'OUP');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Gauss-Seidel Method for Linear Systems.
');
fprintf(1,'The array will be input from a text file in the order
');
fprintf(1,'A(1,1), A(1,2), ..., A(1,n+1),
');
fprintf(1,'A(2,1), A(2,2), ..., A(2,n+1),
');
fprintf(1,'..., A(n,1), A(n,2), ..., A(n,n+1)
');
fprintf(1,'Place as many entries as desired on each line, but separate
');
fprintf(1,'entries with ');
fprintf(1,'at least one blank.
');
fprintf(1,'The initial approximation should follow in same format.
');
fprintf(1,'Has the input file been created? - enter Y or N.
');
AA = input(' ','s');
OK = FALSE;
if AA == 'Y' | AA == 'y'
fprintf(1,'Input the file name in the form - drive:\
ame.ext
');
fprintf(1,'for example: A:\\DATA.DTA
');
NAME = input(' ','s');
INP = fopen(NAME,'rt');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the number of equations - an integer.
');
N = input(' ');
if N > 0
A = zeros(N,N+1);
X1 = zeros(1,N);
for I = 1 : N
for J = 1 : N+1
A(I,J) = fscanf(INP, '%f',1);
end;
end;
% Use X1 for X0
for I = 1 : N
X1(I) = fscanf(INP, '%f',1);
end;
OK = TRUE;
fclose(INP);
else
fprintf(1,'The number must be a positive integer
');
end;
end;
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the tolerance.
');
TOL = input(' ');
if TOL > 0
OK = TRUE;
else
fprintf(1,'Tolerance must be a positive.
');
end;
end;
OK = FALSE;
while OK == FALSE
fprintf(1,'Input maximum number of iterations.
');
NN = input(' ');
if NN > 0
OK = TRUE;
else
fprintf(1,'Number must be a positive integer.
');
end;
end;
else
fprintf(1,'The program will end so the input file can be created.
');
end;
if OK == TRUE
% STEP 1
K = 1;
OK = FALSE;
% STEP 2
while OK == FALSE & K <= NN
% ERR is used to test accuracy - it measures the infinity-norm
ERR = 0;
% STEP 3
for I = 1 : N
S = 0;
for J = 1 : N
S = S-A(I,J)*X1(J);
end;
S = (S+A(I,N+1))/A(I,I);
if abs(S) > ERR
ERR = abs(S);
end;
X1(I) = X1(I) + S;
end;
% STEP 4
if ERR <= TOL
OK = TRUE;
% process is complete
else
% STEP 5
K = K+1;
% STEP 6 - is not used since only one vector is required
end;
end;
if OK == FALSE
fprintf(1,'Maximum Number of Iterations Exceeded.
');
% STEP 7
% procedure completed unsuccessfully
else
fprintf(1,'Choice of output method:
');
fprintf(1,'1. Output to screen
');
fprintf(1,'2. Output to text file
');
fprintf(1,'Please enter 1 or 2.
');
FLAG = input(' ');
if FLAG == 2
fprintf(1,'Input the file name in the form - drive:\
ame.ext
');
fprintf(1,'for example: A:\\OUTPUT.DTA
');
NAME = input(' ','s');
OUP = fopen(NAME,'wt');
else
OUP = 1;
end;
fprintf(OUP, 'GAUSS-SEIDEL METHOD FOR LINEAR SYSTEMS
');
fprintf(OUP, 'The solution vector is :
');
for I = 1 : N
fprintf(OUP, ' %11.8f', X1(I));
end;
fprintf(OUP, '
using %d iterations
', K);
fprintf(OUP, 'with Tolerance %.10e in infinity-norm
', TOL);
if OUP ~= 1
fclose(OUP);
fprintf(1,'Output file %s created successfully
',NAME);
end;
end;
end;
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