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Pentadiagonal matrix
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Pentadiagonal matrix : ウィキペディア英語版
Pentadiagonal matrix
In linear algebra, a pentadiagonal matrix is a matrix that is nearly diagonal; to be exact, it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it. So it is of the form
: \begin
c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\
b_1 & c_2 & d_2 & e_2 & \ddots & & \vdots \\
a_1 & b_2 & \ddots & \ddots & \ddots & \ddots & \vdots \\
0 & a_2 & \ddots & \ddots & \ddots & e_ & 0 \\
\vdots & \ddots & \ddots & \ddots & \ddots & d_ & e_ \\
\vdots & & \ddots & a_ & b_ & c_ & d_ \\
0 & \cdots & \cdots & 0 & a_ & b_ & c_n
\end.
It follows that a pentadiagonal matrix has at most 5n-6 nonzero entries, where ''n'' is the size of the matrix. Hence, pentadiagonal matrices are sparse. This makes them useful in numerical analysis.
==See also==

* tridiagonal matrix

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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