Horner's rule

English

Named after William George Horner, though it significantly pre-dates his work.

Horner's rule

(mathematics, computing theory) The rule stating that a polynomial of degree n can be (optimally) evaluated with only n multiplications and n additions: ${\\displaystyle {\\begin{aligned}a_{0}&+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\\cdots +a_{n}x^{n}\\\\&=a_{0}+x{\\bigg (}a_{1}+x{\\Big (}a_{2}+x{\\big (}a_{3}+\\cdots +x(a_{n-1}+x\\,a_{n})\\cdots {\\big )}{\\Big )}{\\bigg )}.\\end{aligned}}}$

单词	Horner's rule
释义	Horner's rule English Etymology Named after William George Horner, though it significantly pre-dates his work. Proper noun Horner's rule (mathematics, computing theory) The rule stating that a polynomial of degree n can be (optimally) evaluated with only n multiplications and n additions: ${\\displaystyle {\\begin{aligned}a_{0}&+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\\cdots +a_{n}x^{n}\\\\&=a_{0}+x{\\bigg (}a_{1}+x{\\Big (}a_{2}+x{\\big (}a_{3}+\\cdots +x(a_{n-1}+x\\,a_{n})\\cdots {\\big )}{\\Big )}{\\bigg )}.\\end{aligned}}}$ Related terms Horner's method
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