Slove Linear Equations

flowchart and program control flow

Values	Define
A	Coefficient matrix
b	Right side vector
A|b	Augmented matrix which contains coefficient matrix A and right side vector b
iter	Number of iterations
Err_limit	Iterative error
Lax_factor	Relaxation factor
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L	Lower triangular matrix of A
U	Upper triangular matrix of A
R	R=L+U
D	Diagonal matrix of A
M	M=invertD
P	Arrangement matrix
y	Intermediate vector in direct methods and jacobi method
solution	Repersent x, which defined by A·x=b

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Direct methods

• Gaussian elimination method with pivoting
• LU decomposition method with pivoting
• TDMA method with pivoting

control flow and flowcharts of Gaussian elimination

• Input: A|b

control flow and flowcharts of LU decomposition

• Input: A,b

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Iterative methods

• Jacobi method
• Gauss–Seidel method
• Successive over-relaxation method

control flow and flowcharts of Jacobi method

• Input: A,b,iter,Err_limit

control flow and flowcharts of Gauss–Seidel method

• Input: A,b,iter,Err_limit

control flow and flowcharts of Successive over-relaxation method

• Input: A,b,iter,Err_limit,Lax_factor