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Zur Numerik rekurrenter Relationen

Numerical aspects of recurrence relations

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Zusammenfassung

Systeme linearer rekurrenter Relationen erster Ordnung, und auch skalare Rekursionsformeln höherer Ordnung, werden auf numerische Stabilität hin untersucht. Beispiele heftiger Instabilität werden vorgeführt im Zusammenhang mit skalaren Rekursionsformeln erster und zweiter Ordnung. Auf Mittel zur Eliminierung von Instabilität wird hingewiesen.

Summary

Systems of linear first-order recurrence relations, as well as higher-order scalar recurrence relations, are analyzed with respect to numerical stability. Examples of severe numerical instability are presented involving scalar first- and second-order recurrence relations. Devices for counteracting instability are indicated.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, 47907, Lafayette, IN, U.S.A.

    W. Gautschi

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  1. W. Gautschi
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Mit 3 Abbildungen

Erweiterte Fassung eines Vortrages, gehalten an Mathematischen Instituten in Florenz, Pisa, Amsterdam, Hamburg und München. Die Arbeit wurde zum Teil durch ein Fulbright-Forschungs-stipendium gefördert.

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Gautschi, W. Zur Numerik rekurrenter Relationen. Computing 9, 107–126 (1972). https://doi.org/10.1007/BF02236961

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  • DOI: https://doi.org/10.1007/BF02236961