TY - JFULL
AU - Xingping Sheng
PY - 2012/9/
TI - An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
T2 - International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
SP - 899
EP - 904
EM - Xingpingsheng@163.com
VL - 6
SN - 1307-6892
UR - http://waset.org/publications/9544
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 68, 2012
N2 - Let T and S be a subspace of Cn and Cm, respectively.
Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized
inverse A(2)
T,S is given by A(2)
T,S = (PS⊥APT )†. In this paper, a
finite formulae is presented to compute generalized inverse A(2)
T,S
under the concept of restricted inner product, which defined as <
A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this
iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the
generalized inverse A(2)
T,S can be obtained within at most mn iteration
steps in absence of roundoff errors. Finally given numerical example
is shown that the iterative formulae is quite efficient.
ER -