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Increase the number of sample points: The more sample points you collect, the more accurate your interpolation will be. In Python, you can use the numpy.linspace() function to create an array of equally spaced points.

Use higher-order interpolating functions: Higher-order interpolation functions can provide more accurate results. In Python, you can use the scipy.interpolation.interp1d() function to create higher-order interpolating functions.

Use adaptive interpolation: Adaptive interpolation involves using a different interpolation function in different regions of the function. This can provide more accurate results over the entire range of the function. In Python, you can use the scipy.interpolate.PchipInterpolator() function to perform adaptive interpolation.

Use least squares regression: Least squares regression can be used to fit a curve to the data using polynomial or other functions. In Python, you can use the numpy.polyfit() function to perform least squares regression.

Add noise reduction: Interpolation can be affected by noise in the data. You can use a technique such as averaging, filtering or smoothing to reduce the noise. In Python, you can use the scipy.signal.filtfilt() function to perform filtering.