For some operations (esp. Cholesky and triangular solves) LAPACK has routines for rectangular full packed format (newer than the format @nalimilan and @stevengj address above), which
enables the use of half the full storage while maintaining efficiency by using Level 3 BLAS/LAPACK kernels.
(detaiils here, about haflway down the page).
If these capabilities fit the bill, the price to be paid is in developer time.