Pentadiagonal matrix

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

: egin{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 \ 0 & 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} \ 0 & cdots & cdots & 0 & a_{n-2} & b_{n-1} & c_n end{pmatrix}.

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.

ee also

* tridiagonal matrix

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