The paper presents a simple procedure for the construction of quasi-interpolation operators in spaces of m-harmonic splines in R(d), which reproduce polynomials of high degree. The procedure starts from a generator phi(0), which is easy to derive but with corresponding quasi-interpolation operator reproducing only linear polynomials, and recursively defines generators phi(1), phi(2), ... , phi(m-1) with corresponding quasi-interpolation operators reproducing polynomials of degree up to 3. 5 2m - 1 respectively. The construction of phi(j); from phi(j-1) is explicit, simple and independent of m. The special case d = 1 and the special cases d = 2. m = 2, 3,4 are discussed in details.
Bozzini, M., Dyn, N., Rossini, M. (2011). Construction of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 236(4), 557-564 [10.1016/j.cam.2011.07.002].
Construction of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines
BOZZINI, MARIA TUGOMIRA;ROSSINI, MILVIA FRANCESCA
2011
Abstract
The paper presents a simple procedure for the construction of quasi-interpolation operators in spaces of m-harmonic splines in R(d), which reproduce polynomials of high degree. The procedure starts from a generator phi(0), which is easy to derive but with corresponding quasi-interpolation operator reproducing only linear polynomials, and recursively defines generators phi(1), phi(2), ... , phi(m-1) with corresponding quasi-interpolation operators reproducing polynomials of degree up to 3. 5 2m - 1 respectively. The construction of phi(j); from phi(j-1) is explicit, simple and independent of m. The special case d = 1 and the special cases d = 2. m = 2, 3,4 are discussed in details.
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