(( Only Solve Part D )) Use the following iteration-based methods, using Matlab,

Question

(( Only Solve Part D ))

Use the following iteration-based methods, using Matlab, to approximate the solution of the above system. After each iteration the program should check to see if the convergence condition, below, is satisfied for each equation: The integration-based methods to be considered are the following: Gauss Method Gauss-Seidel method Part C is canceled because numerical analysis using Newton-Raphson method was not covered in class Optional (for extra credit) Gauss-Seidel method with acceleration factor (from 1.1 to 1.8)

Explanation / Answer

% Gauss Siedal Method

for j=1:1:size
   stringInput = ('Enter the matrix for the solution ');
   SolMat = input(stringInput);
emd % end of for loop

len = length(SolMat);
ZeroVect = zeros(len,1);
unitVect = ones(len,1);

% test whether the matrix satisfies the property of dominance along the main diagonal

for indexVar1 = 1:len
      indexVar2 = 1:len;
   indexVar2(indexVar1) = [ ];
   AbsVal = abs(matrixOne(indexVar1,indexVar2));
   Check(inedxVar1,1) = abs(matrixOne(indexVar1,indexVar1)) - sum(SolMat);
% compare the diagonal value with the remaining row value
   if Check(indexVar1) < 0
       disp 'The diagonal dominancy property is not satisfied by this matrix'
   end
end

repeat = 0;
while (max(unitVect) > C_n     % look for errors
   repeat = repeat + 1;
   RemembMat = ZeroVect;
   for indexVar1 = 1:len
          indexVar2 = 1:len;     % co efficients here
          indexVar2(indexvar1) = [ ];
          tempZeroMat =    ZeroVect;
          tempZeroMat(indexVar1) = [ ];
          ZeroVect(inedxVar1,1) = (SolMat(indexVar1,1) - sum(matrixOne(indexVar1, indexVar2) * tempZeroMat)) / matrixOne(indexVar1, indexVar1);
   end % end for
   SolZeroMat = ZeroVect;
   unitVect = sqrt((ZeroVect - RemembMat).^2);
end
SolZeroMat
repeat

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