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Preconditioning linearized equations

Präkonditionierung linearisierter Gleichungen

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Abstract

When solving systems of nonlinear equations, generally the first step is to linearize them. When using interval methods, one usually preconditions the linear equations by multiplying by a real (i.e. non-interval) matrix which approximates the inverse of the center of the interval Jacobian. In this paper, we show that it is better to precondition the original nonlinear equations rather than the linearized ones.

Zusammenfassung

Bei der Lösung nichtlinearer Gleichungssysteme wird im allgemeinen zuerst linearisiert. Wenn Intervall-Methoden benützt werden, werden die linearen Gleichungen üblicherweise durch Multiplikation mit geeigneten reellen Zahlen konditioniert. Wir zeigen, daß eine Präkonditionierung der ursprünglichen, nicht linearisierten Gleichungen besser ist.

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Hansen, E.R. Preconditioning linearized equations. Computing 58, 187–196 (1997). https://doi.org/10.1007/BF02684439

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  • DOI: https://doi.org/10.1007/BF02684439

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