TY - JOUR
T1 - Efficient solution of A, x (k) =b (k) using A -1
AU - Ditkowski, Adi
AU - Fibich, Gadi
AU - Gavish, Nir
PY - 2007/7
Y1 - 2007/7
N2 - 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.
AB - 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.
KW - Linear systems
KW - Matrix inversion
UR - http://www.scopus.com/inward/record.url?scp=34250893831&partnerID=8YFLogxK
U2 - 10.1007/s10915-006-9112-x
DO - 10.1007/s10915-006-9112-x
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AN - SCOPUS:34250893831
SN - 0885-7474
VL - 32
SP - 29
EP - 44
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -