IMAC_Articleshttp://hdl.handle.net/10234/1733692019-12-15T07:09:34Z2019-12-15T07:09:34ZSplitting and composition methods with embedded error estimatorsBlanes, SergioCasas, FernandoThalhammer, Mechthildhttp://hdl.handle.net/10234/1849692019-11-18T13:24:08Z2019-12-01T00:00:00ZSplitting and composition methods with embedded error estimators
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the additional computational cost required for their evaluation is almost insignificant. These estimators can be subsequently used to adapt the step size along the integration. Numerical examples show the efficiency of the procedure.
2019-12-01T00:00:00ZContinuous changes of variables and the Magnus expansionCasas, FernandoChartier, PhilippeMurua, Anderhttp://hdl.handle.net/10234/1849022019-11-18T12:53:24Z2019-09-23T00:00:00ZContinuous changes of variables and the Magnus expansion
Casas, Fernando; Chartier, Philippe; Murua, Ander
In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuous variable transformations generated by operators. As an application of the simple formulas so-obtained, we explicitly compute the first terms of the Floquet-Magnus expansion for the Van der Pol oscillator and the nonlinear Schrödinger equation on the torus.
2019-09-23T00:00:00ZFast Algorithms for the Computation of the Minimum
Distance of a Random Linear CodeHernando, FernandoIgual, Francisco D.Quintana Ortí, Gregoriohttp://hdl.handle.net/10234/1844552019-11-18T16:01:04Z2019-06-01T00:00:00ZFast Algorithms for the Computation of the Minimum
Distance of a Random Linear Code
Hernando, Fernando; Igual, Francisco D.; Quintana Ortí, Gregorio
The minimum distance of an error-correcting code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is crucial to many problems in this area. In this article, we present and assess a family of implementations of both the brute-force algorithm and the Brouwer-Zimmermann algorithm for computing the minimum distance of a random linear code over that are faster than current implementations, both in the commercial and public domain. In addition to the basic sequential implementations, we present parallel and vectorized implementations that produce high performances on modern architectures. The attained performance results show the benefits of the developed optimized algorithms, which obtain remarkable improvements compared with state-of-the-art implementations widely used nowadays.
2019-06-01T00:00:00Z[S]-linear and convex structures in function familiesBernal González, L.Conejero, J. AlbertoMurillo-Arcila, MarinaSeoane-Sepúlveda, J. B.http://hdl.handle.net/10234/1840682019-11-18T15:51:29Z2019-01-01T00:00:00Z[S]-linear and convex structures in function families
Bernal González, L.; Conejero, J. Alberto; Murillo-Arcila, Marina; Seoane-Sepúlveda, J. B.
In this paper, the notion of [S]-lineability (originally coined
by Vladimir I. Gurariy) is introduced and developed in a general abstract
setting. This new notion is, then, applied to specific situations, as for
instance, classes of differentiable nowhere monotone functions as well
as families of vectors having dense orbit with respect to an operator.
Large convex structures are also shown to exist inside the family of
topologically mixing continuous selfmaps of a real compact interval.
2019-01-01T00:00:00Z