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The Gauss elimination at the second column can be obtained by multiplying to the relation (2) the lower triangular matrix

Figure 1 The Gauss elimination at the second column can be obtained by multiplying to the relation (2) the lower triangular matrix

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