New algorithms for polynomial and trigonometric interpolation on parallel computers |
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Authors: | Ilan Bar-On Avram Sidi |
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Affiliation: | (1) Department of computer Science, Technion, 32000 Haifa, Israel |
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Abstract: | An interpolation polynomial of orderN is constructed fromp independent subpolynomials of ordern N/p. Each such subpolynomial is found independently and in parallel. Moreover, evaluation of the polynomial at any given point is done independently and in parallel, except for a final step of summation ofp elements. Hence, the algorithm has almost no communication overhead and can be implemented easily on any parallel computer. We give examples of finite-difference interpolation, trigonometric interpolation, and Chebyshev interpolation, and conclude with the general Hermite interpolation problem. |
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