Definition

polynomial interpolation

Polynomial interpolation is a method of estimating values between known data points. When graphical data contains a gap, but data is available on either side of the gap or at a few specific points within the gap, an estimate of values within the gap can be made by interpolation.

The simplest method of interpolation is to draw straight lines between the known data points and consider the function as the combination of those straight lines. This method, called linear interpolation, usually introduces considerable error. A more precise approach uses a polynomial function to connect the points. A polynomial is a mathematical expression comprising a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable. Polynomials can exist in factored form or written out in full. For example:

(x - 4) (x + 2) (x + 10)

x2 + 2x + 1

3y3 - 8y2 + 4y - 2

The value of the largest exponent is called the degree of the polynomial.

If a set of data contains n known points, then there exists exactly one polynomial of degree n-1 or smaller that passes through all of those points. The polynomial's graph can be thought of as "filling in the curve" to account for data between the known points. This methodology, known as polynomial interpolation, often (but not always) provides more accurate results than linear interpolation.

The main problem with polynomial interpolation arises from the fact that even when a certain polynomial function passes through all known data points, the resulting graph might not reflect the actual state of affairs. It is possible that a polynomial function, although accurate at specific points, will differ wildly from the true values at some regions between those points. This problem most often arises when "spikes" or "dips" occur in a graph, reflecting unusual or unexpected events in a real-world situation. Such anomalies are not reflected in the simple polynomial function which, even though it might make perfect mathematical sense, cannot take into account the chaotic nature of events in the physical universe.

This was last updated in April 2013
Contributor(s): Stan Gibilisco
Posted by: Margaret Rouse

Related Terms

Definitions

  • semi-structured data

    - Semi-structured data is data that has not been organized into a specialized format, such as a table, a record, an array or a tree but that nevertheless has associated information, such as metadata,... (WhatIs.com)

  • clinical decision support system (CDSS)

    - A CDSS, or clinical decision support system, is data analysis software or an application that care providers reference during treatment. (SearchHealthIT.com)

  • recommendation engine

    - Recommendation engines are common among online retail websites, such as Amazon. Also known as recommender systems, these applications suggest products (or something else a visitor might search for,... (WhatIs.com)

Glossaries

  • Business intelligence - business analytics

    - Terms related to business intelligence, including definitions about business analytics and words and phrases about gathering, storing, analyzing and providing access to business data.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About polynomial interpolationPowered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment

Share
Comments

    Results

    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.