Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法

摘要t矩阵乘法StraSsen算法及其变形winograd算法用分而治之的方法把矩阵乘法时间复杂性由传统的D(n。)改进到0(佗kg。n.但是对于奇数阶矩阵,在划分子矩阵时,要作特殊处理才能继续使用此算法.本文提出了一种非等阶“十”字架划分方法,可以最少化填零,最大化性能,使得奇数阶矩阵乘法的时间复杂性更加接近偶数阶矩阵乘法的效果.计算实例显示该方法是有效的.     

On the field of definition for modularity of CM elliptic curves

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.     

吸收比-系数倍率法及其应用——水杨酸钠、安替比林和咖啡因的同时测定

用吸收比－系数倍率法同时测定撒痛风注射液中水杨酸钠、安替比林和咖啡因三组分的含量。它们的回收率分别为１００．７％～１０２．１％、９５．９３％～１０４．５％和９７．５７％～１０１．７％。     

双峰倍增配平法用于同步、导数-同步荧光法同时测定邻羟基苯甲酸和间羟基苯甲酸

邻羟基苯甲酸（ｏＨＢＡ）和间羟基苯甲酸（ｍＨＢＡ）荧光光谱严重重叠，同步及导数技术虽使选择性有所改善，但仍不能完全分辨开重叠谱。用双峰倍增配平计算法结合同步、一阶导数－同步荧光法对双组分体系（邻羟基苯甲酸／间羟基苯甲酸，ｐＨ１２介质）同时测定。结合计算的两种测定方法精密度、回收率和不同组分间浓度比范围均优于一阶导数－同步荧光法。     

X=Y=ZH Systems as potential 1,3-dipoles. Part 58: Cycloaddition route to chiral conformationally constrained (R)-pro-(S)-pro peptidomimetics

Imines of (1S,9S)-t-butyl-9-amino-octahydro-6,10-dioxo-6H-pyridazino[1,2-a][1,2]diazepine-1-carboxylate undergo thermal (toluene, 110°C) or LiBr-DBU catalysed (MeCN, room temperature) regio- and stereo-specific cycloaddition to a range of chiral dipolarophiles giving enantiopure spiro-cycloadducts in excellent yield. The reactions proceed via intermediate NH azomethine ylides and litho azomethine ylides, respectively and results in the multiplication of chiral centres from 2 (one of which is lost in the process) to 5.     

测试二元运算乘法表是否构成群表的算法设计

对计算机测试二元运算乘法表是否构成群表的算法进行研究 ,一个乘法表构成群表的充要条件是乘法表具有两个性质·在测试乘法表构成群表的第一性质中提出了直接逐行、逐列测试G中所有元素 ,按行、按列搜索相同元素及相异元素计数三种算法 ;在第二性质测试中 ,对搜索与单位元 1构成矩形的同行、同列元素中提出自然升序法、外推法及小段优先三种算法 ;在遍历整个二维乘法表判别矩形第 4顶点元素特性中 ,提出了单个矩形移动、按行(列 ) (n-1 )个矩形同时移动、(n -1 ) 2 个矩形同时移动及改进的单个矩形移动四种算法 ;讨论了主要算法的复杂性 ;用VisualC ++6.0实现了算法的程序设计 ;用所设计...     

某第二类Fredholm积分方程的一种数值解法

我们考虑第二类 Fredholm积分方程的快速数值解法 .本文假设核函数除在 x=t处带有弱奇性外 ,是解析的 [1] .我们利用分片多项式插值逼近核函数 ,由此得到近似的系数矩阵 A.设 n为积分节点的个数 ,k2为每个小区域的插值节点数 ,我们证明矩阵 A的计算和矩阵 -向量相乘 Ax各需要 O( nk)次运算 ,存贮 A需要占用 O( nk)内存 .最后我们对算法的稳定性进行讨论并给出数值结果     

80位并行3D-DCT硬件核解决方案

提出一种使用三维离散余弦变换 ( 3D DCT)对运动图像进行压缩解压的新算法 .在此算法的基础上构造了一个 80位 3D DCT硬件核 ,通过并行连乘连加运算加快计算速度、三维转置存储体消除矩阵转置耗时、中间寄存器消除中间计算结果的存取时间等综合手段 ,达到高速处理目的 .FPGA实现的时序模拟表明 ,采用这种算法可以对现有制式的电视图像进行实时压解处理 .     

利用矩阵和分块矩阵的乘法计算行列式的值

利用矩阵乘积的行列式公武计算行列式的值;将矩阵巧妙合理地分块后,利用分块矩阵的乘法计算行列式的值.