R: Lagrange Interpolation Polynomials

neville {PolynomF} | R Documentation

## Lagrange Interpolation Polynomials

### Description

Compute the Lagrange Interpolation Polynomial from a given set of x- and y-values, or, alterntively, compute the interpolated values at a set of given x-values. Two algorithms are provided, namely Neville's algorithm, or a more direct version based on the usual Lagrange formula. The latter is generally faster but the former can be more accurate numerically.

### Usage

    neville(x, y, x0 = polynomial())

    lagrange(x, y, x0 = polynomial())

### Arguments

`x` | A numeric vector of x-values
`y` | A numeric values of y-values corresponding to the x-values
`x0` | Either a polynomial object or a vector of x-values for which interpolated y-values are required.

### Value

Either an interpolation polynomial object or a vector of interpolated y-values

### Examples

    set.seed(123)
    x <- 1:5
    y <- rnorm(x)
    xout <- 0.5 + 1:4

    p1 <- neville(x, y)
    plot(p1, xlim = range(x), ylim = extendrange(y, f = 1), panel.first = grid())
    points(x, y, col = 4)
    points(xout, lagrange(x, y, xout), col = 2)

[Package PolynomF version 2.0-5 Index]