Fast and simple modular interpolation using factorial representation

G. L. Mullen; D. Panario; D. Thomson

doi:10.4169/amer.math.monthly.123.5.471

Fast and simple modular interpolation using factorial representation

G. L. Mullen, D. Panario, D. Thomson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study a representation for polynomial functions over finite rings. This factorial representation is particularly useful for fast interpolation, and we show that it is computationally preferable to the Lagrange Interpolation Formula (LIF) and to Newton interpolation over finite fields and rings. Moreover, over arbitrary finite rings the calculation of the factorial representation aborts naturally when a given mapping does not arise as a polynomial function.

Original language	English (US)
Pages (from-to)	471-480
Number of pages	10
Journal	American Mathematical Monthly
Volume	123
Issue number	5
DOIs	https://doi.org/10.4169/amer.math.monthly.123.5.471
State	Published - 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4169/amer.math.monthly.123.5.471

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title = "Fast and simple modular interpolation using factorial representation",

abstract = "We study a representation for polynomial functions over finite rings. This factorial representation is particularly useful for fast interpolation, and we show that it is computationally preferable to the Lagrange Interpolation Formula (LIF) and to Newton interpolation over finite fields and rings. Moreover, over arbitrary finite rings the calculation of the factorial representation aborts naturally when a given mapping does not arise as a polynomial function.",

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AU - Panario, D.

AU - Thomson, D.

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PY - 2016

Y1 - 2016

N2 - We study a representation for polynomial functions over finite rings. This factorial representation is particularly useful for fast interpolation, and we show that it is computationally preferable to the Lagrange Interpolation Formula (LIF) and to Newton interpolation over finite fields and rings. Moreover, over arbitrary finite rings the calculation of the factorial representation aborts naturally when a given mapping does not arise as a polynomial function.

AB - We study a representation for polynomial functions over finite rings. This factorial representation is particularly useful for fast interpolation, and we show that it is computationally preferable to the Lagrange Interpolation Formula (LIF) and to Newton interpolation over finite fields and rings. Moreover, over arbitrary finite rings the calculation of the factorial representation aborts naturally when a given mapping does not arise as a polynomial function.

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DO - 10.4169/amer.math.monthly.123.5.471

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SP - 471

EP - 480

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 5

ER -

Fast and simple modular interpolation using factorial representation

Abstract

All Science Journal Classification (ASJC) codes

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