关于具二次约束最小二乘问题的敏度分析     

刘新国 《中国海洋大学学报(自然科学版)》1996,(2)

本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。  相似文献   

分潮波模型多资料数值计算方法研究　Ⅱ.有限差分最小二乘方法     

潘文波  孙文心  王骥 《中国海洋大学学报(自然科学版)》1996,(2)

对含多资料的分潮波模型的超定问题进行探讨，建立一种有限差分—最小二乘方法，该方法使得岸边资料直接进入了计算方程，并保证岸界法向流速为零条件。通过对渤海的四大分潮的试算，证实本方法可行。  相似文献   

四阶奇异边值问题无穷多个正解存在性的一个注记     

张若君 《中国海洋大学学报(自然科学版)》2002,32(5):848-852

本文考虑四阶奇异边值问题x( 4 ) =λa(t) f (t,x(t) ) ,0 相似文献   

关于多项式特征值的条件数     

刘新国  王学锋 《中国海洋大学学报(自然科学版)》2004,34(5):913-917

Tisseur(2000)研究了非齐次多项式特征值问题的条件数，所得结果的不足是对无穷特征值必须另外处理；Declieu和Tisseur(2003)运用微分几何方法研究了齐次多项式特征值问题的条件数，所得结果的不足之处是与系数矩阵的尺度化(scaling)有关。这两种条件数都有各自的应用范围。本文基于投影尺度引入齐次多项式特征值问题的条件数，其优点是与系数矩阵的尺度化无关，因而也许会有较广泛的应用。  相似文献   

Second order wave diffraction forces and runup by finite—infinite element method     

B.Y. Li  S.L. Lau  C.O. Ng 《Applied Ocean Research》1991,13(6):270-286

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Inverse reconstructions of ecosystem flows in investigating regime shifts: impact of the choice of objective function     

Alain F. Vzina  Florence Berreville  Svetlana Loza 《Progress in Oceanography》2004,60(2-4):321

Inverse analysis is increasingly used in ecosystem modelling to objectively reconstruct a large number of unknown flows or interactions from a small number of observations. This type of analysis may be useful in relating observed regime shifts in ecosystem structure to underlying processes. Inversions of ecosystem flow networks currently use a constrained least-squares solution which at the same time minimizes the squared norm (the sum of squares) of the reconstructed flows. This minimum norm (MN) inversion is thought to be a parsimonious solution to the ecosystem flow inverse problem, but it may well not reflect how ecosystems are organised. It has been proposed instead that ecosystems evolve to maximize energy/mass flows or that they maximize the information content of the network weighted by ecosystem flows (ascendancy). We used simulated inverse experiments, where inverse analyses are applied to simulations of flow networks, to explore objective functions different than the MN generally used. We could not compute inverse solutions that maximize ascendancy because the objective function is unbounded. We could calculate inversions that maximize flows; however, these generally overestimated the simulated flows, even though the simulations were designed to maximize flows. It appears that the ecosystem flow inverse problem is too under-determined (too few data relative to the number of unknowns) to allow the use of these maximizing goal functions. We introduce a new minimization that simultaneously minimizes the squared flows and the squared differences between flows. This smoothing minimization makes the inverse flows as even as possible and it helps with some technical issues with MN inversions. The simulated inverse experiments indicated that this smoothed norm (SM) is the most robust in comparative analyses of contrasting ecosystem states, such as those that can be associated with regime shifts. Like the MN inversion, the SM inversion has no ecological basis. However, it is a conservative norm that is less likely to produce false differences between the dynamics of regimes.  相似文献   

二次特征值问题的最佳向后扰动分析     

杨玉霞  刘新国 《中国海洋大学学报(自然科学版)》2003,33(2):317-323

二次特征值问题 (QEP)的主要的求解方法之一是转化为广义特征值问题 (GEP) ,然后用求解广义特征值的方法 (比如 QZ方法 )求解。本文研究由此获得的计算解的范数意义下的最佳向后扰动分析 ,所得结果是 Tisseur最近所得结果的加强。  相似文献   

一维扩散方程整体观测资料下的初值变分同化反演     

张瑰 《海洋预报》2006,23(Z1):34-41

本文考虑一维扩散方程的反问题,利用变分同化方法通过观测资料来确定方程中的未知初值,通过分析观测误差对于初值误差的影响,证明变分同化初值收敛于原问题的真实参数,并得到了参数的收敛精度。同时将得到的初值代入预报模式中,得到预报解,并分析了预报解的收敛性和预报误差。  相似文献   

一类非线性二阶常微分方程解的多重性     

朴大雄  贺佳 《中国海洋大学学报(自然科学版)》2007,37(6):1039-1044

考虑一类二阶非线性常微分方程的边值问题（p（t）u′）′＋h（t）f（u）=0，0＜t＜1和u（0）=u（1）=0。通过引入f（s）／s在∞与0处的极限值，并运用打靶法和相应的Sturm比较定理得到解的多重性定理，推广有关文献中的许多重要结果。  相似文献   

局部区域GPS网坐标转换的改进模型   总被引：2，自引：1，他引：1  

张秋昭  张书毕  刘军 《全球定位系统》2008,33(5)

GPS的应用经常涉及到坐标变换.用局部小区域的GPS网数据求解三维坐标转换模型(如布尔萨模型)的转换参数时,平移参数精度不高,病态问题较严重.提出了用坐标转换的改进模型,能有效提高平移参数的精度,在一定程度上解决了病态问题,在工程测量中有一定的实用价值.  相似文献