dstech.f - Man Page

subroutine dstech (n, a, b, eig, tol, work, info)
DSTECH

DSTECH

Purpose:

    Let T be the tridiagonal matrix with diagonal entries A(1) ,...,
    A(N) and offdiagonal entries B(1) ,..., B(N-1)).  DSTECH checks to
    see if EIG(1) ,..., EIG(N) are indeed accurate eigenvalues of T.
    It does this by expanding each EIG(I) into an interval
    [SVD(I) - EPS, SVD(I) + EPS], merging overlapping intervals if
    any, and using Sturm sequences to count and verify whether each
    resulting interval has the correct number of eigenvalues (using
    DSTECT).  Here EPS = TOL*MAZHEPS*MAXEIG, where MACHEPS is the
    machine precision and MAXEIG is the absolute value of the largest
    eigenvalue. If each interval contains the correct number of
    eigenvalues, INFO = 0 is returned, otherwise INFO is the index of
    the first eigenvalue in the first bad interval.

Parameters

N

          N is INTEGER
          The dimension of the tridiagonal matrix T.

A

          A is DOUBLE PRECISION array, dimension (N)
          The diagonal entries of the tridiagonal matrix T.

B

          B is DOUBLE PRECISION array, dimension (N-1)
          The offdiagonal entries of the tridiagonal matrix T.

EIG

          EIG is DOUBLE PRECISION array, dimension (N)
          The purported eigenvalues to be checked.

TOL

          TOL is DOUBLE PRECISION
          Error tolerance for checking, a multiple of the
          machine precision.

WORK

          WORK is DOUBLE PRECISION array, dimension (N)

INFO

          INFO is INTEGER
          0  if the eigenvalues are all correct (to within
             1 +- TOL*MAZHEPS*MAXEIG)
          >0 if the interval containing the INFO-th eigenvalue
             contains the incorrect number of eigenvalues.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 100 of file dstech.f.