An analysis on the property of Self-Scaling Rank One Update (SSR1) is given. In view of it, we explore whether the SSR1 update without using exact line search possesses the finite termination property when it is applied to minimize a positive definite quadratic objective function.
1 INTRODUCTION In the end of 1980＇s, an operational system for 3-D variation and assimilation of meteorological data was set up in the U.S.A that supplemented data assimilation, retrieval of satellite data and numerical prediction each other. NWP was thus improved. Towards the end of 1990＇s, satellite observations were extensively used in NWP at ECMWF to upgrade the quality of analysis and forecasting. Subsequently, Chinese meteorologists also made some studies on the analysis and assimilation of satellite data. Jiang et al. were the first to apply satellite imagery in numerical simulation of typhoon-inflicted heavy rain. Shen et al. and Min et al. conducted variational analysis and numerical simulation of conventional soundings and unconventional cloud imagery for limited areas and found that inclusion of cloud imagery could greatly improve rainfall forecast by the model. Zhu et al. suggested that the introduction of satellite-retrieved humidity field could better depict horizontal mesoscale structure of the real world. All of the studies above have achieved lots of meaningful results.
