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dc.contributor.authorLoczi, Lajos
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2015-04-30T12:54:48Z
dc.date.available2015-04-30T12:54:48Z
dc.date.issued2014-05-19
dc.identifier.citationLajos Lóczi and David I. Ketcheson (2014). Rational functions with maximal radius of absolute monotonicity. LMS Journal of Computation and Mathematics, 17, pp 159-205. doi:10.1112/S1461157013000326.
dc.identifier.issn1461-1570
dc.identifier.doi10.1112/S1461157013000326
dc.identifier.urihttp://hdl.handle.net/10754/551012
dc.description.abstractWe study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.
dc.description.sponsorshipThis publication is based on work supported by Award No. FIC/2010/05 – 2000000231, made by King Abdullah University of Science and Technology (KAUST).
dc.language.isoen
dc.publisherOxford University Press (OUP)
dc.relation.urlhttp://www.journals.cambridge.org/abstract_S1461157013000326
dc.relation.urlhttp://arxiv.org/abs/1303.6651
dc.rightsArchived with thanks to LMS Journal of Computation and Mathematics
dc.titleRational functions with maximal radius of absolute monotonicity
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentNumerical Mathematics Group
dc.identifier.journalLMS Journal of Computation and Mathematics
dc.eprint.versionPre-print
dc.identifier.arxividarXiv:1303.6651
kaust.personLoczi, Lajos
kaust.personKetcheson, David I.
refterms.dateFOA2018-06-13T15:34:11Z


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