Barycentric Rational Interpolation

Barycentric rational interpolation is a high-accuracy interpolation method for non-uniformly spaced samples.

Performance and Accuracy:

It requires O(N) time for construction and O(N) time for each evaluation. If the approximation order is d, the error is O(h^(d+1)).

Caveats:

This method is robust but can behave unexpectedly if the sample spacing at the endpoints is much larger than in the center.

Usage

barycentric_rational(x, y, order = 3)

Arguments

x

Numeric vector of data points (abscissas).

y

Numeric vector of data values (ordinates).

order

Integer representing the approximation order of the interpolator, defaults to 3.

Value

An object of class barycentric_rational_interpolator with methods:

• interpolate(xi): Evaluate the interpolator at point xi.

• prime(xi): Evaluate the derivative of the interpolator at point xi.

See also

Boost Documentation

Examples

x <- c(0, 1, 2, 3)
y <- c(1, 2, 0, 2)
order <- 3
interpolator <- barycentric_rational(x, y, order)
xi <- 1.5
interpolator$interpolate(xi)
#> [1] 0.9375
interpolator$prime(xi)
#> [1] -2.291667