The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘采用自主研发的多源多宿GNSS-R(Global Navigation Satellite System-Reflections,全球导航卫星系统反射信号)海洋环境遥感探测系统,在天津渤海湾特定区域进行了3次机载校飞试验,获得了大量有效GNSS-R信号数据,对自然条件下的海面有效波高进行了反演处理。该系统通过对接收的GNSS直达信号和海面反射信号进行相关运算处理,可以获得DDM(Delay-Doppler Mapping,时延—多普勒映射)图谱,再利用DCF(Derivative of the Correlation Function,相关函数的导数)在DDM图谱基础上进行相关功率波形的计算,进而通过计算DCF的函数波形宽度得到海面有效波高,验证了该方法的可行性。该方法具有全天时、全天候、高分辨率、低成本等优点,对全球范围内中小尺度海洋状态和物理现象的监测具有重要意义。
