If is a sparse matrix of the form what is the maximum number of nonzero elements it contains What is the density, where density Such a matrix is termed pentadiagonal. Code a function that applies...

If

is a sparse matrix of the form

what is the maximum number of nonzero elements it contains
What is the density, where density


Such a matrix is termed pentadiagonal.

Code a function

that applies the Gauss-Seidel iteration to solve a system

Your iteration must use only the elements on the five diagonals. Apply the termination criteria

Test your function by solving the

problem

where

is a random matrix generated with the MATLAB command rhs = 100*rand(1000,1). Time the computation. Create the matrix in part

using MATLAB, and solve the system using xmat = A\rhs and compare the two solutions and the time required.