Approximation

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Approximation

Approximation is a process of finding values that are close enough to the correct answer, usually within a specified tolerance. It is a fundamental concept in various fields such as mathematics, physics, engineering, and computer science. Approximations are used when exact values are either unknown or difficult to obtain.

Types of Approximation[edit | edit source]

There are several types of approximations, including:

Applications[edit | edit source]

Approximation is widely used in various applications:

Methods[edit | edit source]

Some common methods of approximation include:

  • **Interpolation**: Estimating values between known data points using methods like linear interpolation and polynomial interpolation.
  • **Extrapolation**: Estimating values outside the range of known data points.
  • **Least Squares Method**: A statistical method used to minimize the differences between observed and predicted values.

Error Analysis[edit | edit source]

Error analysis is crucial in approximation to determine the accuracy and reliability of the approximated values. Common types of errors include:

  • **Absolute Error**: The difference between the exact value and the approximated value.
  • **Relative Error**: The absolute error divided by the exact value, often expressed as a percentage.
  • **Truncation Error**: The error made by truncating an infinite sum and approximating it with a finite sum.

Related Concepts[edit | edit source]

See Also[edit | edit source]

Categories[edit | edit source]


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