Le Cam's theorem: Difference between revisions

Latest revision as of 09:01, 15 August 2014

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-In [[linear algebra]], a '''pentadiagonal matrix''' is a [[matrix (mathematics)|matrix]] that is nearly [[diagonal matrix|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
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-:<math> \begin{pmatrix}
-   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 \\
-& a_2 & \ddots & \ddots & \ddots & e_{n-3} & 0 \\
-   \vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\
-   \vdots & & \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\
-& \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n
-\end{pmatrix}. </math>
-It follows that a pentadiagonal matrix has at most <math>5n-6</math> nonzero entries, where ''n'' is the size of the matrix. Hence, pentadiagonal matrices are [[sparse matrix|sparse]]. This makes them useful in [[numerical analysis]].
-==See also==
-* [[tridiagonal matrix]]
-{{PlanetMath attribution|id=3927|title=Pentadiagonal matrix}}
-[[Category:Sparse matrices]]

Le Cam's theorem: Difference between revisions

Latest revision as of 09:01, 15 August 2014

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