Direct Cardinal Interpolation

Abstract

Direct cardinal interpolation constructs a mean function that intersects given (x, y) points and a variance function that is zero at the points. These functions realize desirable extrapolation and efficiency properties for predicting y given x.  It is found that direct cardinal interpolation is be more efficient than a classic form of Gaussian process interpolation in that its variance is typically much less over the point domain. It is also found that direct cardinal interpolation is less efficient near the end points (points not surrounded by other points); this desirable property is not realized by Gaussian process interpolation. These findings are a consequence of the direct construction of the mean and variance functions so that they achieve desirable properties.