Construction of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines

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• 作者：Mira  ; Bozzini^a ;   ; ^{mira.bozzini@unimib.it} ; Nira  ; Dyn^b ;   ; ^{niradyn@post.tau.ac.il} ; Milvia  ; Rossini^a ;   ; ^{milvia.rossini@unimib.it}
• 关键词：Polyharmonic splines ; Quasi-interpolation operators ; High degree polynomial reproduction ; Rate of decay at infinity ; Approximation order
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2011
• 出版时间：15 September 2011
• 年：2011
• 卷：236
• 期：4
• 页码：557-564
• 全文大小：449 K

文摘

The paper presents a simple procedure for the construction of quasi-interpolation operators in spaces of -harmonic splines in , which reproduce polynomials of high degree. The procedure starts from a generator , which is easy to derive but with corresponding quasi-interpolation operator reproducing only linear polynomials, and recursively defines generators with corresponding quasi-interpolation operators reproducing polynomials of degree up to respectively. The construction of from is explicit, simple and independent of . The special case and the special cases , are discussed in details.