Unformatted text preview: agonals. The ﬁrst n − 1 entries of the
ﬁrst column of “D” store the lower diagonal. The n entries of the second column of
“D” store the main diagonal. The second through the last entries of the third column
of “D” store the upper diagonal. To construct “D”, we ﬁrst create a zero matrix of
dimensions n × 3:
D = zeros(n,3);
Then, we set the ﬁrst n − 2 entries of the ﬁrst column to h1 , h2 , . . . , hn−2 :
D(1:n-2,1) = h(1:n-2);
The (n − 1)th entry of the ﬁrst column has been initialized to zero already. Next, we
set the entries of the second column to 1, 2(h1 + h2 ), . . . , 2(hn−2 + hn−1 ), 1:
D(:,2) = [1; 2*(h(1:n-2)+h(2:n-1)) ;1];
7. (Ex.) Add a line that ﬁlls in the second through the last entries of the third column
of “D” accordingly.
8. Convert the diagonals “D” to an n × n matrix “A” in sparse form. Sparse form is used to
store matrices with many zero entries. In this form, only the non-zero entries and their
locations are stor...
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This document was uploaded on 10/10/2013.
- Fall '13
- Numerical Analysis