1) least-norm anti-symmetric solution
极小范数反对称解
1.
By this iteration method,the solvability of the equation over anti-symmetric X can be determined automatically,when the equation is consistent over anti-symmetric X,its least-norm anti-symmetric solution can be obtained by choosing a special kind of initial iteration matrix.
选取特殊的初始矩阵,可求得极小范数反对称解。
2) least-norm central symmetric solution
极小范数中心对称解
1.
By this iterative method,the solvability of the equations can be determined automatically,its least-norm central symmetric solution can be got within finite steps.
使用该方法不仅可以判断矩阵方程组是否有中心对称解,而且在有中心对称解时,还能够在有限步迭代计算之后得到矩阵方程组的极小范数中心对称解。
3) least-norm reflexive matrix solution
极小范数自反矩阵解
1.
By this iterative method,the solvability of the equations can be determined automatically,and its reflexive matrix solution or least-norm reflexive matrix solution can be got within finite steps.
该算法可以判断矩阵方程组是否有自反矩阵解,并在有自反矩阵解时,可以在有限步迭代计算之后得到矩阵方程组的一个自反矩阵解或者极小范数自反矩阵解。
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：反对称波函数
分子式：
CAS号：
性质：满足反对称性的波函数。对于电子体系而言，波函数对于电子坐标的交换必须是反对称的，否则计算得到的结果并不能正确地反映电子间的费米相关，即相同自旋取向的电子的运动是相互制约的这个事实。利用斯莱特行列式波函数或用反对称化算符作用在试探函数上就可得到反对称波函数。
CAS号：
性质：满足反对称性的波函数。对于电子体系而言，波函数对于电子坐标的交换必须是反对称的，否则计算得到的结果并不能正确地反映电子间的费米相关，即相同自旋取向的电子的运动是相互制约的这个事实。利用斯莱特行列式波函数或用反对称化算符作用在试探函数上就可得到反对称波函数。
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