MATLAB Mathematics - SERC - Index of

Interpolation
the relevant function at the points specified by xi. This is the default method
for the interp1 function.
• Cubic spline interpolation (method = 'spline'). This method fits a different
cubic function between each pair of existing data points, and uses the spline
function to perform cubic spline interpolation at the data points.
• Cubic interpolation (method = 'pchip' or 'cubic'). These methods are
identical. They use the pchip function to perform piecewise cubic Hermite
interpolation within the vectors x and y. These methods preserve
monotonicity and the shape of the data.
If any element of xi is outside the interval spanned by x, the specified
interpolation method is used for extrapolation. Alternatively,
yi = interp1(x,Y,xi,method,extrapval) replaces extrapolated values with
extrapval. NaN is often used for extrapval.
All methods work with nonuniformly spaced data.
Speed, Memory, and Smoothness Considerations
When choosing an interpolation method, keep in mind that some require more
memory or longer computation time than others. However, you may need to
trade off these resources to achieve the desired smoothness in the result:
• Nearest neighbor interpolation is the fastest method. However, it provides
the worst results in terms of smoothness.
• Linear interpolation uses more memory than the nearest neighbor method,
and requires slightly more execution time. Unlike nearest neighbor
interpolation its results are continuous, but the slope changes at the vertex
points.
• Cubic spline interpolation has the longest relative execution time, although
it requires less memory than cubic interpolation. It produces the smoothest
results of all the interpolation methods. You may obtain unexpected results,
however, if your input data is non-uniform and some points are much closer
together than others.
• Cubic interpolation requires more memory and execution time than either
the nearest neighbor or linear methods. However, both the interpolated data
and its derivative are continuous.
The relative performance of each method holds true even for interpolation of
two-dimensional or multidimensional data. For a graphical comparison of
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