MATLAB Mathematics - SERC - Index of

Sparse Matrix Operations
Background information on these iterative methods and incomplete
factorizations is available in [2] and [7].
Eigenvalues and Singular Values
Two functions are available which compute a few specified eigenvalues or
singular values. svds is based on eigs which uses ARPACK [6].
Functions to Compute a Few Eigenvalues or Singular Values
Function
eigs
svds
Description
Few eigenvalues
Few singular values
These functions are most frequently used with sparse matrices, but they can be
used with full matrices or even with linear operators defined by M-files.
The statement
[V,lambda] = eigs(A,k,sigma)
finds the k eigenvalues and corresponding eigenvectors of the matrix A which
are nearest the “shift” sigma. If sigma is omitted, the eigenvalues largest in
magnitude are found. If sigma is zero, the eigenvalues smallest in magnitude
are found. A second matrix, B, may be included for the generalized eigenvalue
problem
Av = λBv
The statement
[U,S,V] = svds(A,k)
finds the k largest singular values of A and
[U,S,V] = svds(A,k,0)
finds the k smallest singular values.
For example, the statements
L = numgrid('L',65);
A = delsq(L);
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