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##

Direct Solvers for Band Matrices

This section is analogous to §10.3.1
for dense matrices:

* is Hermitian definite.*
- In this case Cholesky is the algorithm of choice.
It is implemented in LAPACK computational routines
`xPBTRF` to compute the factorization and
`xPBTRS` to solve using the factorization
(both are combined in LAPACK driver routine `xPBSVX`).
Cholesky is implemented in analogous ScaLAPACK routines
`PxPBTRF`, `PxPBTRS`, and `PxPBSV`.

* is non-Hermitian.*
- In this case Gaussian elimination is the algorithm of choice.
It is implemented in LAPACK computational routines
`xGBTRF` to compute the factorization and
`xGBTRS` to solve using the factorization
(both are combined in LAPACK driver routine `xGBSVX`).
It is implemented in analogous ScaLAPACK routines
`PxGBTRF`, `PxGBTRS`, and `PxGBSV` with partial pivoting, and
`PxDBTRF`, `PxDBTRS`, and `PxDBSV` without pivoting (which
is risker but faster than using pivoting).

No routines exploiting Hermitian indefinite structure are available
(because there is no simple bound on how much the bandwidth can grow
because of pivoting).
No band routines are in MATLAB.
If is Hermitian and the bandwidth is narrow enough
(such as tridiagonal), direct eigensolver methods
from §4.2 should be used.

** Next:** Direct Solvers for Sparse
** Up:** A Brief Survey of
** Previous:** Direct Solvers for Dense
** Contents**
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Susan Blackford
2000-11-20