Numerical Analysis – Linear Equations(I). Hanyang University Jong-Il Park. Linear equations. N unknowns, M equations. coefficient matrix. where. Solving methods. Direct methods Gauss elimination Gauss-Jordan elimination LU decomposition Singular value decomposition …
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Numerical Analysis – Linear Equations(I)
Upper triangular matrix
Lower triangular matrix
1) Augmented matrix의 행을 최대값이 1이 되도록 scaling(=normalization)
2) 첫 번째 열에 가장 큰 원소가 오도록 partial pivoting
3) 둘째 행 이하의 첫 열을 모두 0이 되도록 eliminating
4) 2행에서 n행까지 1)- 3)을 반복
5) backward substitution으로 해를 구함
For each column
Ax = b LUx = b L-1 LUx = L-1 b
U x = c
L L-1 b = Lc
L c = b
By solving the equations (2) and (1) successively, we get the solution x.