Interpolation
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Polynomial interpolation
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constructs a function that matches supplied data points; interpolation estimates between them, extrapolation beyond them.
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Lagrange form uses basis polynomials equal to 1 at one node and 0 at the others.
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Newton divided differences represent the same interpolating polynomial and can be extended when another point is added.
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Image interpolation
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bilinear image resizing blends four corners of a grid cell
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Bicubic interpolation uses a larger neighborhood and smoother cubic behavior.
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interpolation matches the supplied points but does not guarantee that the data or model is accurate.
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Add curve comparison: equally spaced high-degree polynomial interpolation, Chebyshev nodes, and a cubic spline through the same points.
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