In this paper we study the W -weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W -weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W -weighted Drazin inverse is uniformly o...

We propose a method and algorithm for computing the weighted MoorePenrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method or computing the weighted Moore-Penrose inverse for constant matrices, originated in [2...

For the discretization of integral fractional Laplacian $(-\Delta )^s$, $0 < s 1$, based on piecewise linear functions, we present and analyze a reliable weighted residual posteriori error estimator. In order to compensate for lack $L^2$-regularity in regime $3/4 this estimator includes as an additional weight power distance from mesh skeleton. We prove optimal convergence rates $h$-adaptive al...

The ordered weighted average (OWA) is an aggregation operator that provides a parameterized family of operators between the minimum and the maximum. This paper presents the OWA weighted average distance operator. The main advantage of this new approach is that it unifies the weighted Hamming distance and the OWA distance in the same formulation and considering the degree of importance that each...

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capac...

We develop the fuzzy generalized ordered weighted averaging distance (FGOWAD) operator. It is a new aggregation operator that uses the main characteristics of the generalized OWA (GOWA), the ordered weighted averaging distance (OWAD) and uncertain information represented as fuzzy numbers. This operator includes a wide range of distance measures and aggregation operators such as the fuzzy maximu...

Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and the deviation of d from c is minimum. In this paper, we consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation between c and d is defin...

In this paper, we propose an approach to solving for an inverse problem. We try to evaluate a unique solution of an inverse problem by means of the weighted inverse matrix. We have applied our weighted inverse matrix method to searching for the electric field source and Demonstrating the three dimensional electric field distributions. As a result, we have succeeded in evaluating the unique elec...

Multi-label classification is an extension of classical multi-class one, where any instance can be associated with several classes simultaneously and thus the classes are no longer mutually exclusive. It was experimentally shown that the distance-weighted k-nearest neighbour (DWkNN) algorithm is superior to the original kNN rule for multi-class learning. But, it has not been investigated whethe...