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Example 3 Consider the following two systems of linear equations

Figure 5 Example 3 Consider the following two systems of linear equations

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The Gauss elimination at the second column can be obtained by multiplying to the relation (2) the lower triangular matrix
The Gauss elimination at the second column can be obtained by multiplying to the relation (2) the lower triangular matrix
The matricial equation (2) becomes
The matricial equation (2) becomes
0, Gn-1Gn_2+++G2G is an invertible matrix and the equation (3) becomes with L = G;'Gz'---G)!,G_", and we have the decomposition of A as product of lower triangular matrix by an upper triangular matrix
0, Gn-1Gn_2+++G2G is an invertible matrix and the equation (3) becomes with L = G;'Gz'---G)!,G_", and we have the decomposition of A as product of lower triangular matrix by an upper triangular matrix
by the Cholesky method or LU method.
by the Cholesky method or LU method.
Related topics:
MathematicsPure MathematicsGaussian EliminationGauss EliminationCholesky Decomposition
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