Manuals/calci/PENTADIAGONAL

MATRIX("PENTADIAGONAL",order)

• $order$ is the size of the Pentadiagonal matrix.

Description

• This function gives the pentadiagonal matrix of order 3.
• A pentadiagonal matrix is a matrix that is nearly diagonal.
• So it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it.
• The form of pentadiagonal matrix is:

$A={\begin{pmatrix}c_{1}&d_{1}&e_{1}&0&\cdots &\cdots &0\\b_{1}&c_{2}&d_{2}&e_{2}&\ddots &&\vdots \\a_{1}&b_{2}&\cdots &\ddots &\ddots &\ddots &\vdots \\0&a_{2}&\cdots &\ddots &\ddots &e_{n-3}&0\\\vdots &\ddots &\ddots &\ddots &\ddots &d_{n-2}&e_{n-2}\\\vdots &&\ddots &a_{n-3}&b_{n-2}&c_{n-1}&d_{n-1}\\0&\cdots &\cdots &0&a_{n-2}&b_{n-1}&c_{n}\end{pmatrix}}$.

• When n is the size of the matrix, a pentadiagonal matrix has atmost 5n-6 nonzero entries.
• Here MATIRX("pentadiagonal") is showing the penta diagonal matrix of order 3 with the integer numbers.
• Also in Calci users can get a deimal values with positive and negative numbers.
• The syntax is to get the decimal penta diagonal matrix is MATRIX("pentadiagonal:negative") and MATRIX(pentadiagonal:positive")