1) least norm
范数极小
1.
In this algorithm, three objectives, such as minimum cross-entropy, least norm and maximum entropy, were combined and then a novel dynamic weight-coefficient mechanism was adopted.
算法中折衷考虑了图像重建中最小交叉熵、范数极小化以及最大熵3个目标,并建立了一种新的动态权系数迭代法。
2) minimum-norm
极小范数
1.
In this paper,the symmetric solution with minimum-norm of the matrix equation AXB+CYD=E is considered.
本文讨论了方程AXB+CYD=E的矩阵极小范数对称解。
3) L_1 norm minimization
L_1范数极小
4) minimum norm solution
极小范数解
1.
According to the characteristic of the inverse problems of ECT, the minimum norm solution was improved using regularization technique, and the stability of the numerical solution was analyzed via singular value decomposition principle.
在分析极小范数解的基础上,针对电容层析成像(ECT)逆问题的特点,利用正则技巧对其进行改进,并利用奇异值分解定理分析了这种改进的数值稳定作用。
2.
Furthermore,the results were applied to the relative inverse eigenvalue problem,and the minimum norm solution for the inverse eigenvalue problem was presented.
同时也把所得结论应用到相应的逆特征值问题,并给出了逆特征值问题的极小范数解。
3.
By further theoretical proof and analysis, it is concluded that at any k th step, the estimated values of the unknowns converge to the minimum norm solution if the equations composed by the preceding k sample data are compatible equations or minimum norm least square solution in case that they are contradictory equations,Moreover, the solut.
本研究对递推最小二乘算法进行了理论证明及分析,指出了在任意第k步,未知参数估计值收敛于前k组数据的极小范数解(如果前k组数据所组成方程组为相容方程组)或者极小范数最小二乘解(如果前k组数据所组成方程组为矛盾方程组),并且此解是唯一的;仿真结果同样也验证了该结论的正确性。
5) minimum-norm solution
极小范数解
1.
An iterative method for minimum-norm solution of symmetric singular linear equations Ax=b is proposed.
给出了求对称奇异线性方程组Ａｘ＝ｂ极小范数解的迭代算法，其迭代公式为此处／为秩是，ｒ（ｒ＜ｎ）的ｎ阶实对称矩阵，Ｅ为ｎ阶单位阵，ｂ为ｎ维列向量，ｍ为正整数，ε为正实数。
6) least-norm solution
极小范数解
1.
When the equations are consistent,the solutions can be obtained within finite steps in the absence of round off errors,and the least-norm solution can be given by choosing a special initial matrix.
在不考虑舍入误差时,对任意给定初始矩阵,该迭代算法能够在有限步迭代计算之后得到矩阵方程组的解;选取特殊的初始矩阵时可得到矩阵方程组的极小范数解。
2.
Many references have obtained a series important result by means of matrices decompositions,In this paper,we use an iterative method successfully in finding the solution of Matrix Equations A1XB1=C1,A2XB2=C2 and its least-norm solution optimal approximation solution with the help of the method of convergence of conjugate.
本文从解线性代数方程组的共轭梯度法中受到启示,不是采用传统的矩阵分解的方法,而是采用迭代算法给出了求矩阵方程组A1XB1=C1,A2XB2=C2的解、极小范数解及其最佳逼近解的方法。
补充资料：Luxemburg范数
Luxemburg范数
Luxemburg nonn
L峨曰血叱范数〔I一血叱~;J如盆c服6yP住肋p-Ma] 函数 ，‘x!.(M，一、{*:*>o，丁、(，一’x(:))‘:‘1}， G这里M(u)是关于正的u递增的偶凸函数， 怒“一’M(u)一忽u(M(u))一，一0，对“>0，M(“)>0，且G是R”中的有界集.此范数的性质曾由W.A.J.h以油比飞〔11作了研究.L~b鸣范数等价于O正ez范数(见0口厄空间(C旧允2 sP创芜))，且 I{x}I(，)簇1 lx}I，蕊2 11 x 11(、).如果函数M(u)和N(u)是互补(或互为对偶)的(见O市口类(Or比zc地”‘、则 ，，·，，(一sun{)·(!，，‘!，“!:，，，，，《一‘，}·如果z‘(t)是可测子集E CG的特征函数，则 !l:二11‘M、-一下尖二一. ““启”‘川M一’(l/n篮‘E)’
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条