An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
A comparative study of iterative solutions to linear systems arising in quantum mechanics
Journal of Computational Physics
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
Preconditioning of complex symmetric linear systems with applications in optical tomography
Applied Numerical Mathematics
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Most preconditioned iterative methods apply to both real- and complex-valued linear systems. At the same time, most iterative linear solver packages available today focus exclusively on real-valued systems or deal with complex-valued systems as an afterthought. By recasting the complex problem in a real formulation, a real-valued solver can be applied to the equivalent real system. On one hand, real formulations have been dismissed due to their unfavorable spectral properties. On the other hand, using an equivalent preconditioned real formulation can be very effective. We give theoretical and experimental evidence that an equivalent real formulation is useful in a number of practical situations. Furthermore, we show how to use the advanced features of modern solver packages to formulate equivalent real preconditioners that are computationally efficient and mathematically identical to their complex counterparts.The effectiveness of equivalent real formulations is demonstrated by solving ill-conditioned complex-valued linear systems for a variety of large scale applications. Moreover, the circumstances under which certain equivalent real formulations are competitive is more clearly delineated.