Computing quasi-interpolants from the B-form of B-splines
Computing quasi-interpolants from the B-form of B-splines
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DOI：
10.1016/j.matcom.2010.12.005
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
A. Abbadi;M. Ibáñez;D. Sbibih
中科院分区：
文献类型：
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作者：
A. Abbadi;M. Ibáñez;D. Sbibih
在一般情况下，对于一个充分正则的函数，与离散，微分和积分准插值相关的准插值误差的表达式可以导出，涉及一个衡量非再生单项式近似程度的项。该项依赖于定义拟插值的系数的某些表达式，并且已经提出了它的最小化。然而，由此产生的问题是相当复杂的，往往需要一些计算工作。因此，对于由分段多项式函数φ定义的拟插值，我们提出了一个更简单的最小化问题，基于一些相关的分段多项式函数的Bernstein-Bézier表示，导致一类新的拟插值。
In general, for a sufficiently regular function, an expression for the quasi-interpolation error associated with discrete, differential and integral quasi-interpolants can be derived involving a term measuring how well the non-reproduced monomials are approximated. That term depends on some expressions of the coefficients defining the quasi-interpolant, and its minimization has been proposed. However, the resulting problem is rather complex and often requires some computational effort. Thus, for quasi-interpolants defined from a piecewise polynomial function, φ, we propose a simpler minimization problem, based on the Bernstein–Bézier representation of some related piecewise polynomial functions, leading to a new class of quasi-interpolants.