HOUSEHOLDER'S
ALGORITHM
*
* To obtain a symmetric tridiagonal matrix A(n-1) similar
* to the symmetric matrix A = A(1), construct the following
* matrices A(2),A(3),...,A(n-1) where A(K) = A(I,J)**K, for
* each K = 1,2,...,n-1:
*
* INPUT: Dimension n; matrix A.
*
* OUTPUT: A(n-1) (At each step, A can be overwritten.)
INVERSE
POWER METHOD ALGORITHM
*
* To approximate an eigenvalue and an associated eigenvector of the
* n by n matrix A given a nonzero vector x:
*
* INPUT: Dimension n; matrix A; vector x; tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: Approximate eigenvalue MU; approximate eigenvector x
* or a message that the maximum number of iterations was
* exceeded.
POWER METHOD
ALGORITHM
*
* To approximate the dominant eigenvalue and an associated
* eigenvector of the n by n matrix A given a nonzero vector x:
*
* INPUT: Dimension n; matrix A; vector x; tolerance TOL; maximum
* number of iterations N.
*
* OUTPUT: Approximate eigenvalue MU; approximate eigenvector x
* or a message that the maximum number of iterations was
* exceeded.
QR ALGORITHM
*
* To obtain the eigenvalues of a symmetric, tridiagonal n by n matrix
*
* a(1) b(2)
* b(2) a(2) b(3)
* . . .
* . . .
* . . .
* b(n-1) a(n-1) b(n)
* b(n) a(n)
*
*
* INPUT: n; A(1),...,A(n) (diagonal of A); B(2),...,B(n)
* (off-diagonal of A); maximum number of iterations M,
* tolerance TOL.
*
* OUTPUT: Eigenvalues of A or recommended splitting of A, or a
* message that the maximum number of iterations was
* exceeded.
SYMMETRIC
POWER METHOD ALGORITHM
*
* To approximate the dominant eigenvalue and an associated
* eigenvector of the n by n symmetric matrix A given a nonzero vector x:
*
* INPUT: Dimension n; matrix A; vector x; tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: Approximate eigenvalue MU; approximate eigenvector x or
* a message that the maximum number of iterations was
* exceeded.
WIELANDT'S
DEFLATION ALGORITHM
*
* To approximate the second most dominant eigenvalue and an
* associated eigenvector of the n by n matrix A given an
* approximation LAMBDA to the dominant eigenvalue, an
* approximation V to a corresponding eigenvector and a vector X
* belonging to R**(n-1), tolerance TOL, maximum number of
* iterations N.
*
* INPUT: Dimension n; matrix A; approximate eigenvalue LAMBDA;
* approximate eigenvector V belonging to R**n; vector X
* belonging to R**(n-1).
*
* OUTPUT: Approximate eigenvalue MU; approximate eigenvector U or
* a message that the method fails.