DSTECH
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
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.
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.
Arguments
| N |
(input) INTEGER
The dimension of the tridiagonal matrix T.
|
| A |
(input) DOUBLE PRECISION array, dimension (N)
The diagonal entries of the tridiagonal matrix T.
|
| B |
(input) DOUBLE PRECISION array, dimension (N-1)
The offdiagonal entries of the tridiagonal matrix T.
|
| EIG |
(input) DOUBLE PRECISION array, dimension (N)
The purported eigenvalues to be checked.
|
| TOL |
(input) DOUBLE PRECISION
Error tolerance for checking, a multiple of the
machine precision. |
| WORK |
(workspace) DOUBLE PRECISION array, dimension (N)
|
| INFO |
(output) 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. |