The function spdiags extracts and creates sparse band and diagonal matrices and is a generalization of the MATLAB function diag. We will only use one of its various forms. To create a pentadiagonal...

The function spdiags extracts and creates sparse band and diagonal matrices and is a generalization of the MATLAB function diag. We will only use one of its various forms. To create a pentadiagonal matrix, create vectors that specify the diagonals. We will call these diagonals

<sub>1

2

3

4

5</sub>
 where

<sub>1

2</sub>
are the subdiagonals and

<sub>4

5</sub>
are the superdiagonals. For an
 matrix, each vector must have length To create the matrix, execute

The parameter -2:2 specifies that the diagonals are located at offsets
 and
 from the main diagonal.

 Create a
 pentadiagonal matrix with sub- and superdiagonals
^T
and diagonal

^T
 Show the matrix is positive definite, with an approximate condition number of

 Using

₀
 and a random
 apply cg using tol

⁻¹⁴
and maxiter
In each case, output the residual.

 Use precg with the same tolerance and niter
 Output the residual.