1) triple diagonal factorization
三对角分解
1.
The formula for the LDU factorization,Cholesky factorization and triple diagonal factorization of row(column) symmetric matrix are obtained.
给出行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解公式,可极大地减少行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解的计算量与存储量,而且不会丧失数值精度。
2) symmetric triangular factorization
对称三角分解法
1.
A practical symmetric triangular factorization algorithm is presented, which retains good characteristics of general ones such as little operations and simplicity,but extends the application scope.
针对一般对称线性方程组三角分解法的不足，提出了一种实用的对称三角分解法，它保持了一般对称三角分解法计算量少和计算简捷的特点，同时扩大了对称三角分解的适用范围，可求解任何非奇异对称线性方程组。
3) triangular factorization
三角分解
1.
Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.
对于工程计算中常常遇到的一类线性方程组的求解,通过构造特殊分块矩阵并研究其逆矩阵的三角分解,给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组,及极小范数最小二乘解的快速算法,该算法的计算复杂度为O(mn)+O(n2),而一般方法的计算复杂度为O(mn2)+O(n3)。
2.
In order to decrease the computation amount and reduce the triangular factorization error of Hankel matrix and its inverse,a new fast algorithm is presented in terms of the symmetrical structure of Hankel matrix.
为了降低Hankel矩阵及其逆矩阵三角分解算法的计算量和减小这类算法的误差。
3.
A fast algorithm for determining the triangular factorization of a symmetric r-circulant matrix and inverse matrix using O(n~2) operations is presented.
根据r-对称循环矩阵的特殊结构给出了求这类矩阵本身及其逆矩阵三角分解的快速算法,算法的运算量均为O(n2),一般矩阵及逆矩阵三角分解的运算量均为O(n3)。
4) triangular decomposition
三角分解
1.
In order to study a new algorithm for fast triangular decomposition of Toeplitz matrix,using the displacement structure of the special matrix,the necessary and sufficient condition for a matrix decomposing into the product of the lower and upper triangular Toedplitz matrix is given.
为了研究Toeplitz型矩阵一种新的快速三角分解算法,利用特殊矩阵的位移结构,给出了矩阵可分解为下上三角Toeplitz矩阵乘积的充要条件。
2.
For the m×n Cauchy matrix C with full column rank,the explicit expression and the fast algorithm of the minimal norm least square solution to the linear system Cx=b were indirectly obtained by construction of a special block matrix and study of the triangular decomposition of its inverse.
对于秩为n的m×n阶Cauchy矩阵C,通过构造特殊分块矩阵并研究其逆矩阵的三角分解,进而间接地得到了线性方程组Cx=b的极小范数最小二乘解的显式表达式及其快速算法,所需运算量为O(mn)+O(n2),而通常构造法方程组的方法所需运算量为O(mn2)+O(n3),用正交化法虽然避免了构造法方程组,但所需的运算量更大些。
3.
Method of solving inverse matrix by position displacement, which adopts the triangular decomposition principle can help to solve large inverse matrix with computers.
此方法采用矩阵三角分解原理 ,将矩阵表达为分解上、下三角阵的乘积 ,利用上、下三角阵的求逆结果求得原矩阵的逆阵 。
5) Principal of domain decomposition
主对角分解
6) block triangle decomposition
块三角分解
1.
Based on the system balanced block triangle decomposition, a coefficient matrix of system state equations can be of block diagonally dominant by using imbalanced compensating scheme; and therefore, the result of syst.
因此,在系统平衡块三角分解的基础上,利用非平衡补偿方法使系统状态方程的系数矩阵具有块对角优型,使系统模型简化的结果更为理想。
补充资料：块三对角矩阵
分子式：
CAS号：
性质：一种特定形式的分块矩阵(分块矩阵的元素均为子矩阵)，矩阵的主对角线及其相邻对角线上的子矩阵为方阵，其余子矩阵为零矩阵。块三对角矩阵的运算与三对角矩阵类似。
CAS号：
性质：一种特定形式的分块矩阵(分块矩阵的元素均为子矩阵)，矩阵的主对角线及其相邻对角线上的子矩阵为方阵，其余子矩阵为零矩阵。块三对角矩阵的运算与三对角矩阵类似。
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