Instead of having to store the entire matrix, it is only necessary to store the location and value of the off-diagonal element for each matrix. Eventually, the number of eta matrices will become so large that it becomes cheaper to decompose the basis from scratch than continue using the current data structures. This is the step that must occur infrequently. Also, such a refactorization may occur prematurely in an attempt to promote stability if noticeable round-off errors begin to occur. So long as the refactorizations occur less than once every m times, though, the amortized cost of the Sparse Bartels-Golub Method improves significantly to .
Disadvantages also occur as with any attempt at amortization.
The Forrest-Tomlin Method takes the row with the same diagonal entry as the spike and calculates the matrix factor that algebraically cancels each row entry to zero. Calculation of the matrix factors involves a backsolve with U against the row entries that are to be eliminated. If , d is optimal solution. If , d is optimal solution. If for all i , the solution is unbounded.