Abstract
We have developed an extensive theory for construction of basis functions over algebraic elements. The fundamental theorem of Noether and associated algebraic geometry concepts were invaluable in the analysis. It was demonstrated that by appropriate choice of nodes any prescribed degree basis can be constructed for any well-set algebraic element. Practical guidelines were presented for numerical quadrature over elements. The analysis is of interest for its mathematical content and for its resolution of questions of existence and uniqueness of rational basis functions for continuous patchwork approximation over algebraically reticulated regions. The practical utility of this development has yet to be demonstrated.
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Wachspress, E. (2016). Two-Level Computation. In: Rational Bases and Generalized Barycentrics. Springer, Cham. https://doi.org/10.1007/978-3-319-21614-0_10
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DOI: https://doi.org/10.1007/978-3-319-21614-0_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21613-3
Online ISBN: 978-3-319-21614-0
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