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Gauss Elimination by Segments and Multivariate Polynomial Interpolation
WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
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The construction of a polynomial interpolant to data given at finite pointsets or, most generally, to data specified by finitely many linear functionals is considered, with special emphasis on the linear system to be solved. Gauss elimination by segmentsi.e., by groups of columns rather than by columns is proposed as a reasonable means for obtaining a description of all solutions and for seeking out solutions with good properties. A particular scheme, due to Amos Ron and the author, for choosing a particular polynomial interpolating space in dependence on the given data points, is seen to be singled out by requirements of degree-reduction, scale-invariance, and a certain orthogonality requirement. The close connection, between this particular construction of a polynomial interpolant and the construction of an H-basis for the ideal of all polynomials which vanish at the given data points, is also discussed.
APPROVED FOR PUBLIC RELEASE