The Drazin inverse has important applications in matrix theory and fields such as statistics, probability, linear systems theory, differential and difference equations, Markov chains, and control theory ([1, 2, 11]). In [9], Koliha extended the Drazin invertibility in the setting of Banach algebras with applications to bounded linear operators on a Banach space. In this paper, Koliha was able t...

The iterative process, Xn+i = X„i2I — AX„), for computing A-1, is generalized to obtain the generalized inverse. An iterative method for inverting a matrix, due to Schulz [1], is based on the convergence of the sequence of matrices, defined recursively by (1) Xn+x = X„i21 AX«) (n 0, 1, • • ■ ) to the inverse A~l of A, whenever X0 approximates A"1. In this note the process ( 1 ) is generalized t...

In this paper the inverse eigenvalue problem of recovering the real coefficients in a Sturm–Liouville problem with nonselfadjoint boundary conditions depending on the spectral parameter from the eigenvalues is solved using entire-function theory and the solution of a Marchenko integral equation.

We generalize the inverse patchy colloid model that was originally developed for heterogeneously charged particles with two identical polar patches and an oppositely charged equator to a model that can have a considerably richer surface pattern. Based on a Debye-Hückel framework, we propose a coarse-grained description of the effective pair interactions that is applicable to particles with an a...

The aim of this paper is to prove the existence of inverse pairs for a certain class of numbertheoretic functions. An application of the result is also illustrated. The motivation comes from the study of functions such as Ck(n)= £ l and **(»)= I 1 • a>\ (ah...,ak) = l Gould [1] showed that Ck(n) = Hd\nRk(d) and that i^(/0 has an inverse. In [5] a pair of functions similarly related is also stud...

The recursive method for computing the generalized LM inverse of a constant rectangular matrix augmented by a column vector is proposed in [16, 17]. The corresponding algorithm for the sequential determination of the generalized LM -inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM inverse and the algorithm for the computation o...

We investigate the analytic perturbation of generalized inverses. Firstly we analyze the analytic perturbation of the Drazin generalized inverse (also known as reduced resolvent in operator theory). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows us to treat regular and singular perturbations in a unified framework. W...

This article presents the theoretical analysis of Inverse Generalized Exponential Models. The shapes of the properties of the Inverse Generalized Exponential distribution are discussed. Inverse moments of Inverse Generalized Exponential distribution are derived. In this article we have presented the relationship between shape parameter and other properties such probability distribution, distrib...