共查询到17条相似文献,搜索用时 109 毫秒
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高毅 《高等学校计算数学学报》1998,20(3):201-208
1 引言 设为一闭凸锥,f是R~n到自身的一映射.广义互补问题,记作GCP(K,f),即找一向量x满足 GCP(K,f) x∈K,f(x)∈且x~Tf(x)=0,(1) 其中,是K的对偶锥(即对任一K中向量x,满足x~Ty≤0的所有y的集合).该问题首先 由Habetler和Price提出.当K=R_+~n(R~n空间的正卦限),此问题就是一般的互补问题.许多作者已经提出了很多求解线性或非线性互补问题的方法.例如:Dafermos,Fukushima,Harker和Price以及其它如参考文献所列.近年来,何针对单调线性变分不等式提出了一些投影收缩算法. Fang在函数是Lipschitz连续及强单调的条件下,在[3]给出一简单的迭代投影法,在[4]中给出一线性化方法去求解广义互补问题(1).在[3]中,他的迭代模式是 相似文献
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广义Kawahara方程的Cauchy问题 总被引:1,自引:0,他引:1
对初值在Besov空间中的广义Kawahara方程(?)_tu αu~k(?)_xu β(?)_x~3u γ(?)_x~5u=0进行了研究,其中k是大于4的正整数,证明了对任意的1≤q≤∞,其Cauchy问题在Besov空间B_(2,q)~(sk)(R)和B_(2,q)~s(R)中局部适定,这里s_k=(k-8)/2k,s>max(0,s_k);对小初值问题几乎整体适定.并证明了如果β=0或βγ<0,对小初值问题整体适定. 相似文献
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广义Kawahara方程的Cauchy问题 总被引:2,自引:0,他引:2
对初值在Besov空间中的广义Kawahara方程(э)tu+αuk(э)xu+β(э)3xu+γ(э)5xu=0进行了研究,其中k是大于4的正整数,证明了对任意的1≤q≤∞,其Cauchy问题在Besov空间Bsk2,q(R)和Bs2,q(R)中局部适定,这里sk=k-8/2k,s>max(0,sk);对小初值问题几乎整体适定.并证明了如果β=0或βγ<0,对小初值问题整体适定. 相似文献
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考虑高阶张量特征值互补问题,由于求解张量的最大Pareto-特征值是一个NP难问题,关注于Pareto-特征值的估计,并给出若干关于Z-张量和M-张量的Pareto-特征值的性质. 相似文献
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本文考虑一类离散型随机$R_0$ 张量互补问题,利用Fischer-Burmeister函数将问题转化为约束优化问题,并用投影Levenberg-Marquardt方法对其进行了求解。在一般的条件下得到了该方法的全局收敛性,相关的数值实验表明了该方法的有效性。 相似文献
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Quantale矩阵的广义逆及其正定性 总被引:2,自引:0,他引:2
给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画. 相似文献
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The main propose of this paper is devoted to studying the solvability of the generalized order tensor complementarity problem. We define two problems: the generalized order tensor complementarity problem and the vertical tensor complementarity problem and show that the former is equivalent to the latter. Using the degree theory, we present a comprehensive analysis of existence, uniqueness and stability of the solution set of a given generalized order tensor complementarity problem. 相似文献
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V. O. Pelykh 《Journal of Mathematical Sciences》2001,107(1):3592-3596
It is demonstrated that J. Nester's tensor method for proving the theorem on the positive definiteness of gravitational energy in an asymptotically Minkowsky space is equivalent to E. Witten's spinor method, in which the Saint–Witten equation must be completed with a linear term that includes the gradient of a certain scalar potential. A new proof of the theorem on the positive definiteness of energy is proposed. 相似文献
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Recently, the tensor complementarity problem has been investigated in the literature. In this paper, we extend a class of structured matrices to higher-order tensors; the corresponding tensor complementarity problem has a unique solution for any nonzero nonnegative vector. We discuss their relationships with semi-positive tensors and strictly semi-positive tensors. We also study the property of such a structured tensor. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. We also give two equivalent formulations of such a structured tensor. 相似文献
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S.M. Rump 《BIT Numerical Mathematics》2006,46(2):433-452
We present a computational, simple and fast sufficient criterion to verify positive definiteness of a symmetric or Hermitian
matrix. The criterion uses only standard floating-point operations in rounding to nearest, it is rigorous, it takes into account
all possible computational and rounding errors, and is also valid in the presence of underflow. It is based on a floating-point
Cholesky decomposition and improves a known result. Using the criterion an efficient algorithm to compute rigorous error bounds
for the solution of linear systems with symmetric positive definite matrix follows. A computational criterion to verify that
a given symmetric or Hermitian matrix is not positive definite is given as well. Computational examples demonstrate the effectiveness of our criteria.
AMS subject classification (2000) 65G20, 15A18 相似文献
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Cui Lu-Bin Fan Yu-Dong Song Yi-Sheng Wu Shi-Liang 《Journal of Optimization Theory and Applications》2022,192(1):321-334
Journal of Optimization Theory and Applications - In the paper, we are concerned with the existence and uniqueness of solution for tensor complementarity problem (TCP) and tensor absolute value... 相似文献