Efficient solution of A, x ^(k) =b ^(k) using A ^-1

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.