Purpose

LA_PBSV computes the solution to a linear system of equations $AX = B$, where $A$ has band form and is real symmetric or complex Hermitian and, in either case, positive definite, and where $X$ and $B$ are rectangular matrices or vectors. The Cholesky decomposition is used to factor $A$ as

$$A = U^H U \mbox{ if {\bf UPLO} = 'U', or } A = L\:L^H \mbox{ if {\bf UPLO} = 'L'}$$

where $U$ is an upper triangular band matrix and $L$ is a lower triangular band matrix, each with the same number of superdiagonals or subdiagonals as $A$. The factored form of $A$ is then used to solve the above system.