Efficient Solution of A, x(k) = b(k) Using A-1

• Authors: Adi Ditkowski;Gadi Fibich;Nir Gavish
• Venue: Journal of Scientific Computing
• Year: 2007

In this work, we consider the problem of solving $${Ax^{(k)}=b^{(k)}}$$ , $${k=1,\ldots, K}$$ , where b (k+1) = f(x (k)). We show that when A is a full $${n \times n}$$ matrix and $${K\geqslant cn}$$ , where $${c\ll1}$$ depends on the specific software and hardware setup, it is faster to solve $${Ax^{(k)}=b^{(k)}}$$ for $${{k = 1,\ldots, K}}$$ by explicitly evaluating the inverse matrix A 驴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.