Abstract
The goal of this research is to extend and investigate an improved approach for calculating the weighted Moore–Penrose (WMP) inverses of singular or rectangular matrices. The scheme is constructed based on a hyperpower method of order ten. It is shown that the improved scheme converges with this rate using only six matrix products per cycle. Several tests are conducted to reveal the applicability and efficiency of the discussed method, in contrast with its well-known competitors.
Highlights
Constructing and discussing different features of iterative schemes for the calculation of outer inverses is an active topic of current research in Applied Mathematics
Many papers have been published in the field of outer inverses over the past few decades, each having their own domain of validity and usefulness
Let us consider that M and N are two square Hermitian positive definite (HPD) matrices of sizes m and n (m ≤ n) and A ∈ Cm×n
Summary
Constructing and discussing different features of iterative schemes for the calculation of outer inverses is an active topic of current research in Applied Mathematics (for more details, refer to [1,2,3]). In 1920, Moore was a pioneer of this field and published seminal works about the outer inverse [4,5]. The method of partitioning (due to Greville) was a pioneering work in computing generalized inverses, which was re-introduced and re-investigated in [4,7]. This scheme requires a lot of operations and is subject to cancelation and rounding errors. Several applications of computing the WMP inverse can be observed, with some discussion, in the recent literature [8,9]; including applications to the solution of matrix equations.
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