Assumptions: The premise of interpolation rests on the assumption of a smooth, continuous relationship between known data points, serving to approximate unknown values.

Accuracy: The degree of accuracy achieved by the interpolated value is contingent on the quality of known data points and the foundational assumptions regarding the relationship between variables.

Extrapolation vs. Interpolation: A distinction exists between interpolation and extrapolation: the latter pertains to the estimation of values outside the range of known data points. Extrapolation, being generally less reliable and more susceptible to error, differs from interpolation.

Linear interpolation: This technique hinges on the assumption of a linear relationship between known data points and estimates the unknown value by constructing a straight line connecting the two nearest points.

Polynomial interpolation: This method entails fitting a polynomial function to the known data points, with the unknown value estimated via the resultant polynomial equation.

Spline interpolation: This technique, involving the fitting of a piecewise-defined smooth curve through the known data points, can yield a more accurate and flexible approximation for non-linear relationships.

Data analysis: Interpolation proves instrumental in filling gaps in data points, smoothing data series, or estimating values for statistical models.

Computer graphics: Interpolation is employed in computer graphics to foster smooth transitions between colors, textures, or shapes, and to render images at superior resolutions.

Engineering: Interpolation aids engineers in estimating values vital for the design and optimization of systems, including variables in fluid dynamics simulations, temperature or pressure.

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