nag_dsytrs (f07mec) solves a real symmetric indefinite system of linear equations with multiple right-hand sides,

where  has been factorized by f07mdc (nag_dsytrf).

nag_dsytrs (f07mec) is used to solve a real symmetric indefinite system of linear equations , the function must be preceded by a call to f07mdc (nag_dsytrf) which computes the Bunch–Kaufman factorization of .

If , , where  is a permutation matrix,  is an upper triangular matrix and  is a symmetric block diagonal matrix with 1 by 1 and 2 by 2 blocks; the solution  is computed by solving  and then .

If , , where  is a lower triangular matrix; the solution  is computed by solving  and then .

"NE_ALLOC_FAIL"

Dynamic memory allocation failed.

"NE_BAD_PARAM"

On entry, argument  had an illegal value.

"NE_INT"

On entry, . Constraint: .

On entry, . Constraint: .

"NE_INTERNAL_ERROR"

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.

For each right-hand side vector , the computed solution  is the exact solution of a perturbed system of equations , where

  is a modest linear function of , and  is the machine precision.

If  is the true solution, then the computed solution  satisfies a forward error bound of the form

where .

Note that  can be much smaller than .

Forward and backward error bounds can be computed by calling f07mhc (nag_dsyrfs), and an estimate for  () can be obtained by calling f07mgc (nag_dsycon).

The total number of floating-point operations is approximately .

This function may be followed by a call to f07mhc (nag_dsyrfs) to refine the solution and return an error estimate.

The complex analogues of this function are f07msc (nag_zhetrs) for Hermitian matrices and f07nsc (nag_zsytrs) for symmetric matrices.