dstech()

subroutine dstech	(	integer	N,
		double precision, dimension( * )	A,
		double precision, dimension( * )	B,
		double precision, dimension( * )	EIG,
		double precision	TOL,
		double precision, dimension( * )	WORK,
		integer	INFO
	)

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

[in]	N	N is INTEGER The dimension of the tridiagonal matrix T.
[in]	A	A is DOUBLE PRECISION array, dimension (N) The diagonal entries of the tridiagonal matrix T.
[in]	B	B is DOUBLE PRECISION array, dimension (N-1) The offdiagonal entries of the tridiagonal matrix T.
[in]	EIG	EIG is DOUBLE PRECISION array, dimension (N) The purported eigenvalues to be checked.
[in]	TOL	TOL is DOUBLE PRECISION Error tolerance for checking, a multiple of the machine precision.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (N)
[out]	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.