horner's method: meaning, definition, pronunciation and examples

Rare (specialized technical term)
UK/ˈhɔːnəz ˈmɛθəd/US/ˈhɔːrnərz ˈmɛθəd/

Formal, Technical, Academic

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Quick answer

What does “horner's method” mean?

A mathematical algorithm for evaluating polynomials.

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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

strong
apply Horner's methoduse Horner's methodevaluate using Horner's methodHorner's method for polynomial
medium
efficient Horner's methodnested form (of Horner's method)algorithm of Horner's method
weak
simple Horner's methodstandard Horner's methodclassical Horner's method

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

polynomial evaluation algorithm

Neutral

Horner schemenested multiplication

Weak

synthetic division (related but distinct)

Vocabulary

Antonyms of “horner's method”

naive polynomial evaluationdirect substitution 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

Fill in the gap
For computational efficiency, programmers often use to evaluate high-degree polynomials.
Multiple Choice

What is the primary advantage of Horner's method?