In this section we consider a variant of Gaussian elimination in which the coefficient matrix A is written as a product of a lower triangular matrix L and an upper triangular or echelon matrix U. The main advantage of this method over the straightforward algorithm is that it is considerably more economical when we need to solve several systems of the form Ax = b with the same A but different right-hand sides b. An additional, though less practical, advantage is that we gain some insight into the structure of Gaussian elimination in terms of matrix products.
KeywordsGaussian Elimination Lower Triangular Matrix Dominant Eigenvalue Elimination Algorithm Partial Pivoting
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