Consider a linear system described by a banded coefficient matrix of width 5, or a pentdiagonal

1. A copy of the MATLAB program (i.e. m-files) written to solve the assigned problem.
2. A brief document containing the output from this program, including both graphical and textual output. This document should be in PDF format. If the assigned problem required running the program with several input conditions, the output corresponding to each input should be included.
3. A main report document that uses plain, descriptive language to detail: a. The mathematical or algorithmic strategy used to solve the assigned problem. b. How this strategy was implemented in a MATLAB program. c. How the program output should be interpreted as a solution to the problem. There is no length limit or requirement for this document; it must simply be adequate to describe items a, b and c, above. PDF format is preferred.

Consider a linear system described by a banded coefficient matrix of width 5, or a pentdiagonal
system:
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e2 f2 g2 h2
d3 e3 f3 g3 h3
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    
dn −2 en −2 fn −2 gn −2 hn −2
dn −1 en −1 fn −1 gn −1
dn en fn
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x2
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xn
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rn
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Write an algorithm to solve this system that is more efficient than Gauss elimination, in the
manner of the algorithm for tridiagonal systems that we discussed.
(1) Write a program to implement this algorithm. Use this program to solve the system
represented by the pentdiagonal_coefficients.mat and pentdiagonal_constants.mat files
available on the course Piazza site. Find the solution.
(2) Write a program that can solve the same system using naïve Gauss elimination. Find the
solution.
(3) Compare the number of operations used to find the solution in part (1) to those used to
find the solution in part (2). Explain how this difference will scale with the size of the
system.
Note: The data files are both in the standard MATLAB .mat format. You can use the load
function to read the data in these files into your program.