Chapter 2.4, Problem 3SA

Rerun the calculation in Step 1 for $n=10\cdot 2^k$, where $k=1,\mathrm{...},11$ . Make a table of the errors at $x=L$ for each $n$

. For which $n$

is the error smallest? Why does the error begin to increase with n after a certain point? You may want to make an accompanying table of the condition number of A as a function of $n$

to help answer the last question. To carry out this step for large $k$

, you may need to ask MATLAB to store the matrix A as a sparse matrix to avoid running out of memory. To do this, just initialize A with the command A=sparse (n, n), and proceed as before. We will discuss sparse matrices in more detail in the next section.