HP MLIB User's Guide Vol. 2 7th Ed.

676 HP MLIB LAPACK User’s Guide
SLANST/DLANST/CLANHT/ZLANHT Compute norm of symmetric or Hermitian tridiagonal matrix
Name SLANST/DLANST/CLANHT/ZLANHT
Compute norm of symmetric or Hermitian tridiagonal matrix
Purpose These subprograms compute a norm of a real symmetric or complex Hermitian
tridiagonal matrix A. A real matrix is symmetric if A = A
T
, its transpose; a
complex matrix is Hermitian if A = A*, its conjugate transpose.
A matrix A = (a
ij
) is tridiagonal if its nonzero elements lie only on the principal
diagonal (i = j), the subdiagonal (i = j+1), and the superdiagonal (i = j−1) of
the matrix.
Matrix
Storage
The following example illustrates the storage of symmetric or Hermitian
tridiagonal matrices. Consider the following symmetric tridiagonal matrix of
order n =7:
The subdiagonal is stored in array e and the principal diagonal is stored in
array d, as follows:
112100000
2122320000
0323343 0 0 0
0 0 43 44 54 0 0
0 0 0 54 55 65 0
0 0 0 0656676
000007677
i e(i) d(i)
121 11
232 22
343 33
454 44
565 55
676 66
777