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A note on an error estimate for least squares approximation (1986)

Frenzen, C. L.

Springer

BIT 26 (1986), S. 388-391

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ISSN: 1572-9125

Keywords: Primary 41A80 ; Secondary 41A60 ; Least squares approximation ; error estimate

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract An asymptotic expansion is obtained which provides upper and lower bounds for the error of the bestL 2 polynomial approximation of degreen forx n+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 fromx n+1 to anyfεC n+1[−1, 1], provided upper and lower bounds for the modulus off (n+1) are available.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01933718

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