Concept explainers
Rerun the calculation in Step 1 for
. For which
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
to help answer the last question. To carry out this step for large
, 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.
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Numerical Analysis
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