## Suppose we can write

*A*as a product of two matrices:*A*=*LU*, where*L*is__lower triangular__and*U*is__upper triangular__:## Then

*A***x**= (*LU*)**x**=*L*(*U***x**) =**b**, i.e. must solve,- (1)
*L***y**=**b**; (2)*U***x**=**y**

- (1)
## Can

__reuse__*L*&*U*for subsequent calculations.