海水富营养化评价的主成分-聚类分析方法

根据主成分分析和聚类分析理论 ,针对海水富营养化评价因子间的相关性 ,提出了海水富营养化的主成分 -聚类分析综合评价方法 .该方法能根据实测资料对海水富营养化状况客观地分类并计算出评价权值 ,避免了主观随意性 .将其应用于 2 0 0 0年 5月至 2 0 0 1年 5月柘林湾海水富营养化程度的分类与评价 ,结果与实际吻合 .     

第一类Fredholm积分方程的互补解法

正1引言本文考虑如下第一类Fredholm积分方程的数值求解:∫_a~b k(x,t)f(t)dt=g(x),a≤x≤b,(1)其中k(x,t)是平方可积的核函数,g(x)为已知函数,f(x)为待求的未知函数.第一类Fredholm积分方程有广泛的应用背景,如信号处理等;参见文献[10,21]等.在信号处理模型中,g(x)为观测信号,一般存在误差.因此,实际求解的问题为κf+η=g,(2)     

FAST DENSE MATRIX METHOD FOR THE SOLUTION OF INTEGRAL EQUATIONS OF THE SECOND KIND

We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation.     

线性无关向量组的扩充

本文讨论了与最优化方法有关的一个代数问题:给定 R~n 中 k(k相似文献