Horner's Method for Converting an Integer from Base b to Base 10

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Horner's method for expressing a polynomial reduces the number of multiplications and results in greater numerical stability by potentially avoiding the subtraction of large numbers. It is based on successive factorization to eliminate powers of greater than 1.

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Suppose ; then the method gives .

As an application of Horner's method, if is an integer in base , then is the corresponding integer in base 10.

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Contributed by: Izidor Hafner (January 2019)
Open content licensed under CC BY-NC-SA


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