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polynomial interpolation
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Figure 4: Polynomial interpolation. The six points x1, y1, etc., represent values of an unknown function. A third-degree polynomial has been constructed so that four of its values match four of the values of the unknown function. Other third-degree polynomials could be made to match other sets of four values of the unknown function, or a polynomial of higher degree could be found to match all six.
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polynomial interpolation

mathematics
Also known as: interpolating polynomial
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Figure 4: Polynomial interpolation. The six points x1, y1, etc., represent values of an unknown function. A third-degree polynomial has been constructed so that four of its values match four of the values of the unknown function. Other third-degree polynomials could be made to match other sets of four values of the unknown function, or a polynomial of higher degree could be found to match all six.
Figure 4: Polynomial interpolation. The six points x1, y1, etc., represent values of an unknown function. A third-degree polynomial has been constructed so that four of its values match four of the values of the unknown function. Other third-degree polynomials could be made to match other sets of four values of the unknown function, or a polynomial of higher degree could be found to match all six.

Polynomial interpolation is a mathematical technique used to find a polynomial that passes through a given set of data points. If you have n + 1 points (xi, yi), polynomial interpolation finds a unique polynomial of degree n or less, denoted as p(x), such that p(xi) = yi for each point. This polynomial can then be used to estimate the function's value at points between the known data points. This method is fundamental in numerical analysis for approximating functions and solving various mathematical problems.12

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  1. interpolation
  2. numerical analysis

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