nag_zpptrs (f07gsc) solves a complex Hermitian positive-definite system of linear equations with multiple right-hand sides,

where  has been factorized by f07grc (nag_zpptrf), using packed storage.

nag_zpptrs (f07gsc) is used to solve a complex Hermitian positive-definite system of linear equations , the function must be preceded by a call to f07grc (nag_zpptrf) which computes the Cholesky factorization of  using packed storage. The solution  is computed by forward and backward substitution.

If , , where  is upper triangular; the solution  is computed by solving  and then .

If , , where  is lower triangular; 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 f07gvc (nag_zpprfs), and an estimate for  () can be obtained by calling f07guc (nag_zppcon).

The total number of real floating-point operations is approximately .

This function may be followed by a call to f07gvc (nag_zpprfs) to refine the solution and return an error estimate.

The real analogue of this function is f07gec (nag_dpptrs).