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Polynomial least squares approximations with Ill-conditioned bases

Polynomiale Näherungen zu Kleinsten Fehlerquadraten bei ungünstig beschaffenen Basen

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Abstract

In this note we point out that polynomial least squares approximations may be unstable in coefficient space and stable inL 2. That is, an ill-conditioned basis may produce large errors in particular coefficients yet theL 2 error is small. An explanation of this phenomenon is offered.

Zusammenfassung

Wir zeigen, daß polynomiale Näherungen zu Kleinsten Fehlerquadraten, die im Koeffizientenraum labil sind, inL 2 stabil sein können. Eine ungünstige Basis kann also grobe Fehler für gegebene Koeffizienten liefern, obwohl der FehlerL 2 klein ist. Eine Erklärung dieses Phänomens wird vorgeschlagen.

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Research partially supported by a Rutgers University Research Council Grant.

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Richter, G.R., Steiger, W.L. Polynomial least squares approximations with Ill-conditioned bases. Computing 19, 85–88 (1977). https://doi.org/10.1007/BF02260743

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  • DOI: https://doi.org/10.1007/BF02260743

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