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:

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

• 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")

Examples

• 1.MATRIX("pentadiagonal") =22
• 2.MATRIX("pentadiagonal",3)

-58	15	-4
-54	55	-75
21	-25	-64

• 3.MATRIX("pentadiagonal",6)

54	-56	-28	0	0	0
62	-96	-82	-49	0	0
15	23	20	30	94	0
0	80	95	76	-82	66
0	0	-60	-27	-82	-87
0	0	0	-43	19	89

• 4.MATRIX("pentadiagonal:negative",4)

-59.92012487258762	-79.75753229111433	-20.13208125717938	0
-47.0609312877059	-7.832704461179674	-29.973211092874408	-12.44902245234698
-47.85296192858368	-67.0970072504133	-53.094227402471006	-84.4662182033062
0	-12.941046571359038	-31.090207281522453	-52.342877350747585

• 5.MATRIX("pentadiagonal:positive",5)

86.68749532662332	69.28418821189553	15.4073191806674	0	0
35.21442376077175	31.06112303212285	35.75007226318121	77.74382838979363	0
24.096227367408574	42.69053868483752	98.5696179093793	5.866385693661869	81.69623236171901
0	80.96880922093987	67.79956801328808	45.05093654152006	71.03362120687962
0	0	32.176876766607165	47.92787255719304	48.10425683390349

See Also

• SYMMETRIC
• BIDIAGONAL
• TRIANGULAR

References

• Pentadiagonal Matrix