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If your bandwidth is small, a direct method will be by far the fastest, and if implemented with iterative refinement can provide the solution to almost working accuracy unless the condition is so poor that no method provides any accuracy.
As your matrix is positive definite, it is easy to implement a direct banded method - because of poor condition, increase all pivots smaller than 13-8 times the largest diagonal element to this value before continuing the factorization to increase numerical stability. I would use the resulting factorization as the preconditioner of a conjugate gradient method, then you get the best of both worlds.Answer from Arnold Neumaier on Stack Exchange