Numerical Method20775 marksMatrix factorization and Solving System of Linear Equations
Discuss the Doolittle LU decomposition method for matrix factorization.
Discuss the Doolittle LU decomposition method for matrix factorization. [5]
The coefficient matrix A of a system of linear equations can be decomposed (factorized) into two triangular matrices L (lower triangular) and U (upper triangular) such that: $$A = L \cdot U$$ $$L = \begin{bmatrix} 1 & 0 & 0 \ l{21} & 1 & 0 \ l{31} & l{32} & 1 \end{bmatrix}, \quad U = \begin{bma...