Computing {2,4} and {2,3}-inverses by using the Sherman–Morrison formula

Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates

“…Lemma 1 reveals some of basic properties of the sequence . Following the notation from [20], the notation ℎ ∈ L(ℎ 1 , . .…”

“…In order to present the finite recursive algorithm for computing the Moore-Penrose inverse of with the help of the actual SR1 update formulas (20) and 21, we first define 0 = O ∈ C × . For each = 1, .…”

“…Theorem 5. Let the matrix be defined as in (3), the matrix sequence defined in (14), and the matrix sequence defined in (20). Then the following recursive relations are true:…”

“…Using this method, the authors of [16] proposed a finite method for computing the minimum-norm leastsquares solution of the linear system = . The results derived in [20] reveal that both the SR1 updates techniques and the S-M recursive rule are useful tools in the computation of various matrix products involving the Moore-Penrose inverse of certain symmetric matrices. Particularly, the algorithms introduced in [20] are numerically efficient in computation of {2, 4} and {2, 3} inverses.…”

A survey of gradient methods for solving nonlinear optimization

“…A few modifications of the scheme (3.26) were promoted in [94,96,97,112,114]. The iterations defined in [112] are of the form (3.26), in which γ k I is the Hessian approximation, where γ k = γ(x k , x k−1 ) > 0 is the parameter.…”