Browse Definitions :
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

Continue Reading About polynomial interpolation

SearchCompliance
  • OPSEC (operations security)

    OPSEC (operations security) is a security and risk management process and strategy that classifies information, then determines ...

  • smart contract

    A smart contract is a decentralized application that executes business logic in response to events.

  • compliance risk

    Compliance risk is an organization's potential exposure to legal penalties, financial forfeiture and material loss, resulting ...

SearchSecurity
  • What is cybersecurity?

    Cybersecurity is the protection of internet-connected systems such as hardware, software and data from cyberthreats.

  • private key

    A private key, also known as a secret key, is a variable in cryptography that is used with an algorithm to encrypt and decrypt ...

  • DOS (disk operating system)

    A DOS, or disk operating system, is an operating system that runs from a disk drive. The term can also refer to a particular ...

SearchHealthIT
SearchDisasterRecovery
  • What is risk mitigation?

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • change control

    Change control is a systematic approach to managing all changes made to a product or system.

  • disaster recovery (DR)

    Disaster recovery (DR) is an organization's ability to respond to and recover from an event that affects business operations.

SearchStorage
  • RAID 6

    RAID 6, also known as double-parity RAID, uses two parity stripes on each disk. It allows for two disk failures within the RAID ...

  • RAM (Random Access Memory)

    RAM (Random Access Memory) is the hardware in a computing device where the operating system (OS), application programs and data ...

  • NOR flash memory

    NOR flash memory is one of two types of non-volatile storage technologies.

Close