An iterative algorithm to compute the Bott-Duffin inverse and generalized Bott-Duffin inverse

作者：Sheng Xingping^*

来源：Filomat, 2012, 26(4): 769-776.

DOI：10.2298/FIL1204769S

• Bott-Duffin inverse
• generalized Bott-Duffin inverse
• iterative method
• orthogonal projection

Let L be a subspace of C-n and PL be the orthogonal projector of C-n onto L. For A epsilon C-nxn, the generalized Bott-Duffin (B-D) inverse A((L))((+)) is given by A((L))((+))= PL(APL + PL.)+. In this paper, by defined a nonstandard inner product, a finite formulae is presented to compute Bott-Duffin inverseA((L))((-1)) = P-L(AP(L)+ P-L)(-1) and generalized Bott-Duffin inverseA((L))((+)) = PL(AP(L)+ P-L.)+ under the conditionAis L-zero (i. e., A(L)n (L). = {0}). By this iterative method, when taken the initial matrix X0 = P(L)A* P-L, the Bott-duffin inverse A(-1) (L) and generalized Bott-duffin inverse A((L))((+)) can be obtained within a finite number of iterations in absence of roundoff errors. Finally a given numerical example illustrates that the iterative algorithm dose converge.

• 出版日期2012-11
• 单位阜阳师范学院