horner's method: meaning, definition, pronunciation and examples
Rare (specialized technical term)Formal, Technical, Academic
Quick answer
What does “horner's method” mean?
A mathematical algorithm for evaluating polynomials.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical algorithm for evaluating polynomials.
A computational technique used for efficient polynomial evaluation, root approximation (especially in conjunction with Newton's method), and polynomial division.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling may follow regional conventions (e.g., 'methodise' vs. 'methodize' in derivative words, but the term itself is invariant).
Connotations
Neutral technical term in both varieties.
Frequency
Equally rare outside of mathematics, engineering, and computer science contexts in both regions.
Grammar
How to Use “horner's method” in a Sentence
[Subject] applies Horner's method to [Polynomial Object] to obtain [Result].[Subject] uses Horner's method for [Purpose, e.g., evaluation].Vocabulary
Collocations
Examples
Examples of “horner's method” in a Sentence
verb
British English
- We shall hornerise the polynomial to find its value at x=3.
- The coefficients were hornered for efficiency.
American English
- We need to hornerize the polynomial before coding the algorithm.
- The software horners the input automatically.
adverb
British English
- The polynomial was evaluated Horner-wise.
- He computed the value Hornersly.
American English
- She solved it Horner-fashion.
- Proceed Hornerly to avoid errors.
adjective
British English
- The Horner-form representation is more compact.
- We used a Horner-based approach.
American English
- The Horner-style evaluation is preferred.
- This is a Horner-type algorithm.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Primarily in mathematics, computer science, and engineering textbooks, papers, and lectures.
Everyday
Never used.
Technical
Core term in numerical analysis, computer algebra systems, and algorithm design.
Vocabulary
Synonyms of “horner's method”
Strong
Neutral
Weak
Vocabulary
Antonyms of “horner's method”
Watch out
Common Mistakes When Using “horner's method”
- Misspelling as 'Horners' method' (missing apostrophe).
- Confusing it with synthetic division (which is a related application for polynomial division).
- Using it for non-polynomial functions.
FAQ
Frequently Asked Questions
It is named after William George Horner (1786-1837), though similar algorithms were known to Chinese mathematicians and Paolo Ruffini.
No, it is fundamental in computer science for writing efficient code to evaluate polynomials, as it minimizes the number of multiplications and additions.
It is the rearranged form of a polynomial, e.g., ax³+bx²+cx+d is rewritten as ((ax + b)x + c)x + d, which reveals the sequence of operations.
Not directly. It is primarily for evaluation. However, it is often used in conjunction with root-finding algorithms like Newton's method, where efficient evaluation of the polynomial and its derivative is required.
A mathematical algorithm for evaluating polynomials.
Horner's method is usually formal, technical, academic in register.
Horner's method: in British English it is pronounced /ˈhɔːnəz ˈmɛθəd/, and in American English it is pronounced /ˈhɔːrnərz ˈmɛθəd/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None. It is a technical term, not used idiomatically.”
Learning
Memory Aids
Mnemonic
HORNER: How One Rapidly Numbers Every Root. Think of nesting coefficients like a set of nested Russian dolls.
Conceptual Metaphor
COMPUTATION IS EFFICIENCY. The method metaphorically 'unpacks' a polynomial in the most economical way.
Practice
Quiz
What is the primary advantage of Horner's method?