4.4.2 L-U Factorization While Gaussian methods are easy to understand and are reliable, better methods are introduced to improve efficiency and computer memory U is an upper triangular matrix with nonzero diagonal elements L is a lower triangular matrix with nonzero diagonal elements A-LU L-U Factorization Ax=LUx=b is solved by transforming into Ly=b Ux=y4.4.2 L-U Factorization While Gaussian methods are easy to understand and are reliable, better methods are introduced to improve efficiency and computer memory U is an upper triangular matrix with nonzero diagonal elements L is a lower triangular matrix with nonzero diagonal elements A  LU L-U Factorization Ax  LUx  b is solved by transforming into Ly  b Ux  y