sparse matrix - Linear iterative solver vs direct solver stability -


is iterative solver more stable direct solver based on lu factorization. lu based solver, have cond(a) < cond(l) * cond(u), factorization amplifies numerical inaccuracy. in event of ill conditioned matrix a, condition number large 1e10, better off using iterative solver stability , numerical accuracy?

there 2 factors involved answering question.

1) physical system analyzing ill-conditioned (in mechanical terms, system pretty "loose", equilibrium state may vary depending on small variation in boundary conditions)

2) physical system ok, matrix has not been scaled before solution process begins.

in first case, there isn't can do: physical system inherently unstable. consider applying different boundary conditions, example. in second case, preconditioner should helpful; example, jacobi preconditioner makes matrix having diagonal values equal 1. in case, iterations more converge.the condition ratio of 1e10 shouldn't represent trouble, provided preconditioning used.


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