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In this paper we present a survey of various algorithms for computing matrix geometric means and derive new second-order optimization algorithms to compute the Karcher mean. These new algorithms are constructed using the standard definition of the Riemannian Hessian. The survey includes the ALM list of desired properties for a geometric mean, the analytical(More)
When computing an average of positive definite (PD) matrices, the preservation of additional matrix structure is desirable for interpretations in applications. An interesting and widely present structure is that of PD Toeplitz matrices, which we endow with a geometry originating in signal processing theory. As an averaging operation, we consider the(More)
MOTIVATION Various approaches based on features extracted from protein sequences and often machine learning methods have been used in the prediction of protein folds. Finding an efficient technique for integrating these different protein features has received increasing attention. In particular, kernel methods are an interesting class of techniques for(More)
s at ICCAM 2012 Multi-Step Skipping Methods with Modified Search Direction for Unconstrained Optimization Nudrat Aamir Department of Mathematical Sciences, University of Essex Wivenhoe Park, Colchester, Essex, CO4 3SQ United Kingdom naamir@essex.ac.uk Joint work with: John A. Ford When dealing with unconstrained non-linear optimization problems using(More)
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