High Quality Content by WIKIPEDIA articles! In the mathematical discipline of linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant.Generally, a matrix equation Ax=b is the general problem of n linear simultaneous equations to solve. If A is an mtimes n Toeplitz matrix, then the system is rather special (has only m+n-1 degrees of freedom, rather than m n). One could therefore expect that solution of a Toeplitz system would be easier.Two Toeplitz matrices may be added in O(n) time. A Toeplitz matrix can be multiplied by a vector in O(n log n) time, and the matrix multiplication of two Toeplitz matrices can be done in O(n2) time.Toeplitz systems of form Ax = b can be solved by the Levinson-Durbin Algorithm in (n2) time. Variants of this algorithm have been shown to be weakly stable (i.e., they exhibit numerical stability for well-conditioned linear systems).

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.