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dc.contributor.authorMunthe-Kaas, Hanseng
dc.contributor.authorQuispel, Reinouteng
dc.contributor.authorZanna, Antonellaeng
dc.description.abstractA remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature and their tangents. This theory can be used to unify a range of different topics, such as polar-type matrix decompositions, splitting methods for computation of the matrix exponential, composition of selfadjoint numerical integrators and dynamical systems with symmetries and reversing symmetries. The thread of this paper is the following: involutive automorphisms on groups induce a factorization at a group level, and a splitting at the algebra level. In this paper we will give an introduction to the mathematical theory behind these constructions, and review recent results. Furthermore, we present a new Yoshida-like technique, for self-adjoint numerical schemes, that allows to increase the order of preservation of symmetries by two units. The proposed techniques has the property that all the time-steps are positive.en_US
dc.rightsAttribution CC BYeng
dc.subjectgeometric integrationeng
dc.subjectsymmetric spaceseng
dc.subjectdifferential equationseng
dc.titleSymmetric spaces and Lie triple systems in numerical analysis of differential equationsen_US
dc.typePeer reviewed
dc.typeJournal article
dc.rights.holderCopyright The Author(s) 2014en_US
dc.source.journalBIT Numerical Mathematics

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