SSVDCT
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N
tridiagonal matrix T which are less than or equal to SHIFT. T is
formed by putting zeros on the diagonal and making the off-diagonals
equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N). If SHIFT is
positive, NUM is equal to N plus the number of singular values of a
bidiagonal matrix B less than or equal to SHIFT. Here B has diagonal
entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1).
If SHIFT is negative, NUM is equal to the number of singular values
of B greater than or equal to -SHIFT.
See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford University,
July 21, 1966
tridiagonal matrix T which are less than or equal to SHIFT. T is
formed by putting zeros on the diagonal and making the off-diagonals
equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N). If SHIFT is
positive, NUM is equal to N plus the number of singular values of a
bidiagonal matrix B less than or equal to SHIFT. Here B has diagonal
entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1).
If SHIFT is negative, NUM is equal to the number of singular values
of B greater than or equal to -SHIFT.
See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford University,
July 21, 1966
Arguments
| N |
(input) INTEGER
The dimension of the bidiagonal matrix B.
|
| S |
(input) REAL array, dimension (N)
The diagonal entries of the bidiagonal matrix B.
|
| E |
(input) REAL array of dimension (N-1)
The superdiagonal entries of the bidiagonal matrix B.
|
| SHIFT |
(input) REAL
The shift, used as described under Purpose.
|
| NUM |
(output) INTEGER
The number of eigenvalues of T less than or equal to SHIFT.
|