Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

FBS Linkage ontology and technique to support engineering change management

© 2014, Springer-Verlag London. Engineering changes are essential for any product development, and their management has become a crucial discipline. Research in engineering change management has brought about some methods and tools to support dealing with changes. This work extends the change prediction method through incorporation of a function–behaviour–structure (FBS) scheme. These additional levels of detail provide the rationales for change propagation and allow a more proactive management of changes. First, we develop the ontology of this method based on a comprehensive comparison of three seminal functional reasoning schemes. Then, we demonstrate the FBS Linkage technique by applying it to a diesel engine. Finally, we evaluate the method.