Abstract
In many research areas like structural mechanics, economics, meteorology, and fluid dynamics, problems are mapped to large sparse linear systems via discretization. The resulting matrices are often ill-conditioned with condition numbers of about 1016 and higher. Usually these systems are preconditioned before they are fed to an iterative solver.
Especially for ill-conditioned systems, we show that we have to be careful with these three classical steps — discretization, preconditioning, and (iterative) solving. For Krylov subspace solvers we give some detailed analysis and show possible improvements based on a multiple precision arithmetic. This special arithmetic can be easily implemented using the exact scalar product — a technique for computing scalar products of floating point vectors exactly.
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© 1999 Springer Science+Business Media Dordrecht
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Facius, A. (1999). Influences of Rounding Errors in Solving Large Sparse Linear Systems. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_2
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DOI: https://doi.org/10.1007/978-94-017-1247-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5350-3
Online ISBN: 978-94-017-1247-7
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