Order relations for concave interpolation methods
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Abstract In this note, we derive relationships between interpolation methods that use a concave interpolation function f . In particular, when the two given data points to be interpolated lie on a line with a negative slope, we show that linear interpolation returns a higher value than f -linear interpolation which in turn yields a higher value than f - f interpolation. These results are useful in comparing interpolation methods commonly used in science and engineering, such as linear, log-linear, and log–log interpolation.
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