Positive definite indistinguishability operators

Aggregating with Indistinguishability Operators

Finitely Valued Indistinguishability Operators

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

Karcher Means and Karcher Equations of Positive Definite Operators

The Karcher or least-squares mean has recently become an important tool for the averaging and studying of positive definite matrices. In this paper we show that this mean extends, in its general weighted form, to the infinite-dimensional setting of positive operators on a Hilbert space and retains most of its attractive properties. The primary extension is via its characterization as the unique...

Robust Multilevel Methods for General Symmetric Positive Definite Operators

An abstract robust multilevel method for solving symmetric positive definite systems resulting from discretizing elliptic partial differential equations is developed. The term “robust” refers to the convergence rate of the method being independent of discretization parameters, i.e., the problem size, and problem parameters. Important instances of such problem parameters are in particular (highl...

Error Representation Formula for Eigenvalue Approximations for Positive Definite Operators

The main contribution of this paper is an error representation formula for eigenvalue approximations for positive definite operators defined as quadratic forms. The formula gives an operator theoretic framework for treating discrete eigenvalue approximation/estimation problems for unbounded positive definite operators independent of the multiplicity. Furthermore, by the use of the error represe...