In this work, we consider the problem of solving x (k) =b (k), k= 1,...K,where b (k+1) = f(x (k)). We show that when A is a full n × n matrix and K ≥cn, where c≦ 1 depends on the specific software and hardware setup, it is faster to solve Ax (k) =b (k) for k = 1,...K by explicitly evaluating the inverse matrix A -1 rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.
- Linear systems
- Matrix inversion