Error Estimates for the Cardinal Spline Interpolation | Zendy

Gennadi Vainikko | Zendy

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Error Estimates for the Cardinal Spline Interpolation

Author(s) -

Gennadi Vainikko

Publication year - 2009

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1381

Subject(s) - spline interpolation , mathematics , spline (mechanical) , interpolation (computer graphics) , statistics , computer science , artificial intelligence , bilinear interpolation , engineering , motion (physics) , structural engineering

For the Sobolev class W per (R) of 1-periodic functions, an unimprovable error estimate for the spline interpolants of order m on the uniform grid is known. In the present paper, this error estimate is extended to the Sobolev class V m,∞(R) of (nonperiodic) functions on R having bounded mth derivative. Some further error estimates are established including the error estimates for derivatives of the spline interpolant.

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