J. R. Gilbert and S. Toledo. An assessment of incomplete-LU preconditioners for nonsymmetric linear systems. Technical report, Xerox Palo Alto Research Center, Palo Alto, CA, 1997.  Home/Search   Document Details and Download   Summary   Related Articles

....for solving many nonsymmetric and indefinite matrices, despite the fact that their existence in these applications is not guaranteed. However, their failure rates are still too high for them to be used as blackbox library software for solving general sparse matrices of practical interests [9, 25]. In fact, the lack of robustness of preconditioned iterative methods is currently the major impediment for them to gain acceptance in industrial applications, in spite of their intrinsic advantage for large scale problems. For indefinite matrices, there are at least two reasons that make ILU ....

....and direct method (preconditioners) Our idea of constructing preconditioners from the point of view of direct solver is therefore justified. Such a viewpoint directly pinpoints to the major weakness of current iterative methods, i.e. their lack of robustness. As Gilbert and Toledo remarked [25], current iterative solvers are not as robust as the state of the art direct solvers to be used as blackbox solvers. More robust preconditioners may be developed by extracting robustness strength from strategies used in modern direct solvers. We conducted analyses on simplified model problems to ....

J. R. Gilbert and S. Toledo. An assessment of incomplete-LU preconditioners for nonsymmetric linear systems. Technical report, Xerox Palo Alto Research Center, Palo Alto, CA, 1997.

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