Local Spline Approximation Methods.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The construction of explicit polynomial spline approximation operators for real-valued functions defined on intervals or on reasonably behaved sets in higher dimensions is studied. The operators take the form Qf the summation of lambda sub i f N sub i, where the N sub i are B-splines and the lambda sub i are appropriate linear functionals. Explicit operators are found which apply to wide classes of functions including continuous or integrable functions. Moreover, the operators are local and approximate smooth functions with an accuracy comparable to best spline approximation. They can be constructed without matrix inversion, local as well as global error bounds are obtained, and some of the error bounds are free of mesh restrictions. Author
- Numerical Mathematics