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9544

An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

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.

Generalized inverse A(2)
T,S, Restricted inner product,
Iterative method, Orthogonal projection.