J4 ›› 2011, Vol. 46 ›› Issue (12): 96-103.
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田治平
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TIAN Zhi-ping
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摘要：
利用多项式快速算法,给出了首加尾循环线性系统求解的快速算法。当首加尾循环矩阵非奇异时,该算法求首加尾循环线性系统的惟一解,当首加尾循环矩阵奇异时,该算法求首加尾循环线性系统的特解和通解。最后,利用首加尾循环矩阵与首加尾向后循环矩阵之间的关系,给出了首加尾向后循环线性系统求解的快速算法。
关键词: 首加尾循环线性系统;快速算法;惟一解;通解
Abstract:
A fast algorithm for solving the first plus last circulant linear system is presented by the fast algorithm for computing polynomials. When the first plus last circulant matrix is nonsingular, we compute its unique solution. When the first plus last circulant matrix is singular, we compute its special solution and general solution. Finally, a fast algorithm for solving the first plus last retrocirculant linear system is proposed by using the relationship between the first plus last circulant matrix and the first plus last retrocirculant matrix.
Key words: the first plus last circulant linear system; fast algorithm; unique solution; general solution
田治平. 首加尾循环线性系统求解的快速算法[J]. J4, 2011, 46(12): 96-103.
TIAN Zhi-ping. Fast algorithm for solving the first plus last circulant linear system[J]. J4, 2011, 46(12): 96-103.
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