Symmetric Subresultants and Applications

Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dichotomic process and FFT is designed. We prove also that these symmetric sub-resultants have a deep link with Toeplitz matrices. Finally, we propose a new algorithm of inversion for such matrices. It has the same cost as those already known, however it is fraction-free and consequently well adapted to computer algebra

Separation des modules et des arguments des zeros d'un polynome

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 81287 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Modeling Land Surface Fluxes from Uncertain Rainfall: A Case Study in the Sahel with Field-Driven Stochastic Rainfields

International audienceIn distributed land surface modeling (LSM) studies, uncertainty in the rainfields that are used to force models is a major source of error in predicted land surface response variables. This is particularly true for applications in the African Sahel region, where weak knowledge of highly time/space-variable convective rainfall in a poorly monitored region is a considerable obstacle to such developments. In this study, we used a field-based stochastic rainfield generator to analyze the propagation of the rainfall uncertainty through a distributed land surface model simulating water and energy fluxes in Sahelian ecosystems. Ensemble time/space rainfields were generated from field observations of the local AMMA-CATCH-Niger recording raingauge network. The rainfields were then used to force the SEtHyS-Savannah LSM, yielding an ensemble of time/space simulated fluxes. Through informative graphical representations and innovative diagnosis metrics, these outputs were analyzed to separate the different components of flux variability, among which was the uncertainty represented by ensemble-wise variability. Scale dependence was analyzed for each flux type in the water and energy budgets, producing a comprehensive picture of uncertainty propagation for the various flux types, with its relationship to intrinsic space/time flux variability. The study was performed over a 2530 km 2 domain over six months, covering an entire monsoon season and the subsequent dry-down, using a kilometer/daily base resolution of analysis. The newly introduced dimensionless uncertainty measure, called the uncertainty coefficient, proved to be more effective in describing uncertainty patterns and relationships than a more classical measure based on variance fractions. Results show a clear scaling relationship in uncertainty coefficients between rainfall and the dependent fluxes, specific to each flux type. These results suggest a higher sensitivity to rainfall uncertainty for hydrological than for agro-ecological or meteorological applications, even though eddy fluxes do receive a substantial part of that source uncertainty