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