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Linear Mapping (linear + mapping)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Computability of solutions of operator equations

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4-5 2007
Volker Bosserhoff
Abstract We study operator equations within the Turing machine based framework for computability in analysis. Is there an algorithm that maps pairs (T, u) (where T is given in form of a program) to solutions of Tx = u ? Here we consider the case when T is a bounded linear mapping between Hilbert spaces. We are in particular interested in computing the generalized inverse T,u, which is the standard concept of solution in the theory of inverse problems. Typically, T, is discontinuous (i. e. the equation Tx = u is ill-posed) and hence no computable mapping. However, we will use effective versions of theorems from the theory of regularization to show that the mapping (T, T *, u, ,T,u ,) , T,u is computable. We then go on to study the computability of average-case solutions with respect to Gaussian measures which have been considered in information based complexity. Here, T, is considered as an element of an L2 -space. We define suitable representations for such spaces and use the results from the first part of the paper to show that (T, T *, ,T,,) , T, is computable. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A Generalized Discriminant Rule When Training Population and Test Population Differ on Their Descriptive Parameters

BIOMETRICS, Issue 2 2002
Christophe Biernacki
Summary. Standard discriminant analysis methods make the assumption that both the labeled sample used to estimate the discriminant rule and the nonlabeled sample on which this rule is applied arise from the same population. In this work, we consider the case where the two populations are slightly different. In the multinormal context, we establish that both populations are linked through linear mapping. Estimation of the nonlabeled sample discriminant rule is then obtained by estimating parameters of this linear relationship. Several models describing this relationship are proposed and associated estimated parameters are given. An experimental illustration is also provided in which sex of birds that differ morphometrically over their geographical range is to be determined and a comparison with the standard allocation rule is performed. Extension to a partially labeled sample is also discussed. [source]

On the norms of quaternionic extensions of real and complex linear mappings

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2007
Daniel Alpay
Abstract We study the connections between the norms of bounded operators on real and complex normed spaces, and with range in quaternionic spaces, and of their quaternionic extensions. We study some aspects of the relations between the quaternionization and the complexification of an inner product real space. The problems that arise when k -linear mappings are defined for the quaternionic case, are considered too. Copyright © 2006 John Wiley & Sons, Ltd. [source]