MATLAB Mathematics - SERC - Index of

6 Sparse Matrices
set up the five-point Laplacian difference operator on a 65-by-65 grid in an
L-shaped, two-dimensional domain. The statements
size(A)
nnz(A)
show that A is a matrix of order 2945 with 14,473 nonzero elements.
The statement
[v,d] = eigs(A,1,0);
computes the smallest eigenvalue and eigenvector. Finally,
L(L>0) = full(v(L(L>0)));
x = -1:1/32:1;
contour(x,x,L,15)
axis square
distributes the components of the eigenvector over the appropriate grid points
and produces a contour plot of the result.
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1 −0.5 0 0.5 1
The numerical techniques used in eigs and svds are described in [6].
6-40