A note on an error estimate for least squares approximation View Full Text


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Article Info

DATE

1986-09

AUTHORS

C. L. Frenzen

ABSTRACT

An asymptotic expansion is obtained which provides upper and lower bounds for the error of the bestL2 polynomial approximation of degreen forxn+1 on [−1, 1]. Because the expansion proceeds in only even powers of the reciprocal of the large variable, and the error made by truncating the expansion is numerically less than, and has the same sign as the first neglected term, very good bounds can be obtained. Via a result of Phillips, these results can be extended fromxn+1 to anyfεCn+1[−1, 1], provided upper and lower bounds for the modulus off(n+1) are available. More... »

PAGES

388-391

References to SciGraph publications

  • 1975-12. An error estimate for least squares approximation in BIT NUMERICAL MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01933718

    DOI

    http://dx.doi.org/10.1007/bf01933718

    DIMENSIONS

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