SUMMARYIn statistical long-range forecasting the large volume of data makes some form of filtering imperative both to reduce the data-handling problem and to exclude random elements which do not contribute to understanding or prediction. In this study, which is an exercise in the statistical technique of factor analysis, fields of 30-day surface temperature anomaly for the years 1881-1960 are filtered in terms of sets of patterns specific to each calendar month. These are derived empirically, and so truly reflect the characteristics of the original fields. In the resulting representation, the volume of data may be reduced to one quarter while retaining 80 per cent of the original variance, and a study of seasonal variation shows that continentality and zonal thermal advection are at all times of year the most important factors in shaping the 30-day anomaly fields.
Long‐term global integrations of the primitive equations for the free‐surface model are performed using spherical polar co‐ordinates. Two methods are used to overcome the computational drawback of excessive resolution near the poles. In the first, time‐steps vary latitudinally on a grid with constant angular increments. Stable integrations result, in which the evolutions closely match (save for phase‐truncation due to divergence) those of the analytic solution of the non‐divergent vorticity equation for initial data in which non‐linear interactions vanish. In the second set of integrations zonal resolution varies latitudinally, and the resulting differential phase‐truncation causes spurious interactions which lead to rapid departure from the analytic solution. In both cases finite difference approximations are used which preserve domain sums of mass and of total energy (kinetic plus potential), in analogy with properties of the continuous equations. The space‐differencing method, together with the time‐smoothing inherent in the variable time‐step scheme, may have helped to suppress non‐linear instability in the first set of integrations.
We give a survey on packages for multiple precision interval arithmetic, with the main focus on three specific packages. One is within a Maple environment, intpakX, and two are C/C++ libraries, GMP-XSC and MPFI. We discuss their different features, present timing results and show several applications from various fields, where high precision intervals are fundamental.
Keywords:Multiple precision interval arithmetic, packages, ease of use, efficiency, reliability.
RésuméDans cet article est effectué un tour d'horizon des outils implémentant l'arithmétique par intervalles en précision multiple. Un coup de projecteur est donné sur trois de ces outils. Le premier est un paquetage développé pour Maple: intpakX, les deux autres sont des bibliothèques C/C++: GMP-XSC et MPFI. Leurs spécificités sont présentées, puis leurs performances sont données. Enfin, sont développées quelques applications, issues de domaines d'application divers, pour lesquelles l'arithmétique par intervallesà grande précision est fondamentale.
AbstractintpakX, a Maple package for interval arithmetic created in 1999 by I. Geulig and W. Krämer [1,3], is based on intpak, an experimental Maple package that was created by A.E. Connell and R.M. Corless in 1993 [2].intpakX contains basic data types and operators for interval arithmetic as well as a variety of numerical methods using intervals. It offers the possibility to compute verified numerical results with a Computer Algebra System and at the same time display the results graphically.With the new version intpakX v1.0, intpakX has been updated and redesigned to work with Maple7. This paper shows the range of features of intpakX and gives some examples of their use.
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