An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
نویسنده
چکیده
Let T and S be a subspace of C and C, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = C, the generalized inverse A T,S is given by A (2) T,S = (PS⊥APT ) †. In this paper, a finite formulae is presented to compute generalized inverse A 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 = PTAPS⊥ , the generalized inverse A 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. Keywords—Generalized inverse A T,S , Restricted inner product, Iterative method, Orthogonal projection.
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