Xingping Sheng An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
900 - 904
2012
6
8
International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering http://waset.org/publications/9544
http://waset.org/publications/68
World Academy of Science, Engineering and Technology
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.
International Science Index 68, 2012