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An imbedding method of iteration with global convergence

Ein iteratives Einbettungsverfahren mit globaler Konvergenz

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Summary

In the solution methods introduced byDavidenko andGavurin the nonlinear equation is simulated by an initial value problem involving a differential equation. In this paper a related imbedding method has been presented, where a sequence of locally convergent iteration processes produces a global convergence even without any knowledge of a first approximation.

Zusammenfassung

In den vonDawidenko undGawurin eingeführten Lösungsmethoden simuliert man die nichtlineare Gleichung mit einem Anfangswertproblem einer Differentialgleichung. In diesem Aufsatz wird ein verwandtes Einbettungsverfahren angeführt, wo eine Reihe von lokal konvergenten Iterationsprozessen die globale Konvergenz auch ohne Kenntnis über die erste Approximation herzustellen vermag.

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References

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Dedicated to Professor Dr.L. Collatz, in honour of his 60th birthday

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Laasonen, P. An imbedding method of iteration with global convergence. Computing 5, 253–258 (1970). https://doi.org/10.1007/BF02248025

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Keywords

  • Differential Equation
  • Computational Mathematic
  • Nonlinear Equation
  • Solution Method
  • Global Convergence