1C Program for Gauss Elimination Method _ Code With C

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C Program for Gauss Elimination MethodMarch 28, 2014 in Numerical Methods 5 Comments

In engineering and science, the solution oflinear simultaneous equations is veryimportant. Different analysis such as electroniccircuits comprising invariant elements, anetwork under steady and sinusoidalcondition, output of a chemical plant andfinding the cost of chemical reactions in suchplants require the solution of linearsimultaneous equations.

In Gauss-Elimination method, these equationsare solved by eliminating the unknownssuccessively. The C program for Gausselimination method reduces the system to anupper triangular matrix from which theunknowns are derived by the use of backward substitution method.

Pivoting, partial or complete, can be done in Gauss Elimination method. So, this method is somewhatsuperior to the Gauss Jordan method. This approach, combined with the back substitution, is quitegeneral. It is popularly used and can be well adopted to write a program for Gauss Elimination Methodin C.

For this, let us first consider the following three equations:

a1x + b1y + c1z = d1a2x + b2y + c2z = d2a3x + b3y + c3z = d3

Assuming a1 0, x is eliminated from the second equation by subtracting (a2/ a1) times the first equationfrom the second equation. In the same way, the C code presented here eliminates x from third equationby subtracting (a3/a1) times the first equation from the third equation.

Then we get the new equations as:

a1x + b1y + c1z = d1b2y + c2z = d2c3z = d3

The elimination procedure is continued untilonly one unknown remains in the lastequation. After its value is determined, theprocedure is stopped. Now, GaussElimination in C uses back substitution toget the values of x, y and z as:

z= d3 / c3y=(d2 c2z) / b2x=( d1- c1z- b1y)/ a1

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SourceCodeforGaussEliminationMethodinC:

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Also see,Gauss Elimination Algorithm and FlowchartNumerical Methods Tutorial Compilation

The source code for Gauss Elimination in C needs to compiled in Code::Blocks. The program is tested andis bug-free. If you have any queries regarding Gauss Elimination Method or its program aforementioned,bring them up from the comments box.

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#includeint main(){ int i,j,k,n; float A[20][20],c,x[10],sum=0.0; printf("\nEnter the order of matrix: "); scanf("%d",&n); printf("\nEnter the elements of augmented matrix row-wise:\n\n"); for(i=1; i



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Previous:C Program for Fixed Point IterationMethod Next:C Program for Gauss-Jordan Method

December 16, 2014 at 8:08 pmPatrik

Please, what is meaning of: x[n]=A[n][n+1]/A[n][n]; I dont get itReply

November 26, 2014 at 7:32 pmAnonymous

Can you also include the function of partial pivoting in this program?Reply

September 4, 2014 at 12:36 pmPavan

your program is not working for some special matrices , u should improve the program in such a way thatit has to work for all types of matrices

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September 4, 2014 at 1:32 pmPramesh Pudasaini

Really? What do you mean by some special matrices?Reply

November 30, 2014 at 10:50 amPassingBy

E.g. matrix, where at some point element on the main diagonal will be equal 0.You should try https://en.wikipedia.org/wiki/Elementary_matrix#Operations

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1C Program for Gauss Elimination Method _ Code With C