Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1311-4815-6 |
Объём: | 112 страниц |
Масса: | 190 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
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).
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