Purpose

LA_SYSV computes the solution to a linear system of equations $A\,X = B$, where $A$ is a real or complex symmetric matrix and $X$ and $B$ are rectangular matrices or vectors. A diagonal pivoting method is used to factor $A$ as

$$A = U\, D\, U^T \mbox{ if {\bf UPLO} = 'U', or } A = L\,D\,L^T \mbox{ if {\bf UPLO} = 'L'}$$

where $U$ (or $L$) is a product of permutation and unit upper (or lower) triangular matrices, and $D$ is a symmetric block diagonal matrix with $1 \times 1$ and $2 \times 2$ diagonal blocks. The factored form of $A$ is then used to solve the above system.
LA_HESV computes the solution to a linear system of equations $A\,X = B$, where $A$ is a complex Hermitian matrix and $X$ and $B$ are rectangular matrices or vectors. A diagonal pivoting method is used to factor $A$ as

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

where $U$ (or $L$) is a product of permutation and unit upper (or lower) triangular matrices, and $D$ is a complex Hermitian block diagonal matrix with $1 \times 1$ and $2 \times 2$ diagonal blocks. The factored form of $A$ is then used to solve the above system.