- (c) Use the Gaussian elimination with partial pivoting to determine a permutation matrix P, a unit lower triangular matrix L, and an upper triangular matrix U such that P A = LU. Determine the growth factor ρ. (d) Use the factorization P A = LU computed in (c) to solve the system of linear equations Ax = b.
- When doing Gaussian Elimination, we say that the growth factor is: U∞ A∞. Partial Pivoting. Unfortunately, using complete pivoting requires about twice as many oating point opera-tions as partial pivoting. Therefore, since partial pivoting works well in practice, complete pivoting is hardly ever...
- Section 5.3 LU factorization with (row) pivoting. 5.3.1 Gaussian elimination with row exchanges; 5.3.2 Permutation matrices; 5.3.3 LU factorization with partial pivoting; 5.3.4 Solving A x = y via LU factorization with pivoting; 5.3.5 Solving with a triangular matrix; 5.3.6 LU factorization with complete pivoting; 5.3.7 Improving accuracy via ...

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