Pentadiagonal matrix - Alchetron, The Free Social Encyclopedia

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

( c 1 d 1 e 1 0 ⋯ ⋯ 0 b 1 c 2 d 2 e 2 ⋱ ⋮ a 1 b 2 ⋱ ⋱ ⋱ ⋱ ⋮ 0 a 2 ⋱ ⋱ ⋱ e n − 3 0 ⋮ ⋱ ⋱ ⋱ ⋱ d n − 2 e n − 2 ⋮ ⋱ a n − 3 b n − 2 c n − 1 d n − 1 0 ⋯ ⋯ 0 a n − 2 b n − 1 c n ) .

It follows that a pentadiagonal matrix has at most 5 n − 6 nonzero entries, where n is the size of the matrix. Hence, pentadiagonal matrices are sparse. This makes them useful in numerical analysis.

References

Pentadiagonal matrix Wikipedia

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