A Lie triple system is a subspace of a Lie algebra closed under the ternary composition [[xy]z]; equivalently, it may be defined as the subspace of elements mapped into their negatives by an automorphism of order two in a Lie algebra; or, finally, a Lie triple system may be defined by a set of identities. A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of 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 self adjoint numerical integrators and dynamical systems with symmetries and reversing symmetries.
Review articles are the summary of current state of understanding on a particular research topic. They analyze or discuss research previously published by scientist and academicians rather than reporting novel research results. Review article comes in the form of systematic reviews and literature reviews and are a form of secondary literature. Systematic reviews determine an objective list of criteria, and find all previously published original research papers that meet the criteria. They then compare the results presented in these papers. Literature reviews, by contrast, provide a summary of what the authors believe are the best and most relevant prior publications. The concept of "review article" is separate from the concept of peer-reviewed literature. It is possible for a review to be peer-reviewed, and it is possible for a review to be non-peer-reviewed.
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Last date updated on October, 2020