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Ruffini-Horner Algorithm for Complex Arguments

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Suppose we need to calculate a value of the polynomial with real coefficients for the complex argument . We divide the polynomial by , where and . The remainder is then a linear function and the value of the polynomial is the value of the remainder. In the table, that is the value at the bottom right.

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The table is defined as follows, where the last row is the sum of the higher rows:

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Contributed by: Izidor Hafner (June 2017)
Open content licensed under CC BY-NC-SA

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According to [1, p. 1034] this is called the Collatz contribution.

Reference

[1] D. Kurepa, Higher Algebra, Book 2 (in Croatian), Zagreb: Skolska knjiga, 1965.

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