This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise TLSE are derived. Computable expressions upper bounds these also given avoid costly Kronecker product-based operations. The results unify ones TLS problem. For problems equilibratory input data, n...

This paper provides a lexical entry schema for exclusives covering the adverbs only, just, exclusively, merely, purely, solely, simply, and the adjectives only, sole, pure, exclusive and alone. We argue, on the basis of inter-paraphrasability relations among these exclusives and entailments involving at least and at most, that all of these items make an at-issue contribution of an upper bound o...

1 This work (Sycadi project) was supported by Region Rhones-Alpes, France Abstract: In this paper, a linear matrix equality (LMI) based H∞ filtering formulation is presented for fault detection and isolation (FDI) problems of linear time-invariant descriptor systems. The fixed-order H∞ FDI filter design is characterized in terms of definite LMIs with no equality constraint, which are done recen...

A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-M...

A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...