摘要
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.
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. The amount of computation by the method is O （ mn ） ＋ O（n^2）, while the amount of computation is O（ mn^2） ＋ O （ n^3） by conventional method for construction of the normal equations. The amount of computation for the orthogonalization method is further increased, although it avoids the construction of the normal equations.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2005年第6期725-728,共4页
Journal of Hohai University(Natural Sciences)
基金
陕西省自然科学基金资助项目(2004CS110002)
