Construction of optimal order nonlinear solvers using inverse interpolation
MetadataShow full item record
There is a vast literature on finding simple roots of nonlinear equations by iterative meth- ods. These methods can be classified by order, by the information used or by efficiency. There are very few optimal methods, that is methods of order 2m requiring m + 1 function evaluations per iteration. Here we give a general way to construct such methods by using inverse interpolation and any optimal two-point method. The presented optimal multi- point methods are tested on numerical examples and compared to existing methods of the same order of convergence.
Applied Mathematics and Computation, 217, (2010), 2448-2455.The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.07.045
Showing items related by title, author, creator and subject.
Arnason, G.; Haltiner, G.J.; Frawley, M.J. (1962-05);Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence ...
Kelly, J.F.; Giraldo, Francis X.; Constantinescu, E.M. (2013);We derive an implicit-explicit (IMEX) formalism for the three-dimensional Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud-resolving and mesoscale (flow in a 3D ...
Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data Chu, P.C.; Fan, C.W. (Springer, 2017);Two distinct layers usually exist in the upper ocean. The rst has a near-zero vertical gradient in temperature (or density) from the surface and is called the iso-thermal layer (or mixed layer). Beneath that is a layer ...