comphy (version 1.0.5)

nevaitpol: Neville-Aitken algorithm for polynomial interpolation

Description

Hierarchical series of linearly-interpolated \(P_{ij}\) values calculated using Neville-Aitken's algorithm. In the \(P_{ij}\) expression, j is the level of the algorithm and i the leftmost grid-point of the tabulated function points.

Usage

nevaitpol(x, f, x0)

Value

An upper triangular matrix of size n containing the linearly-interpolated values. P[i,j] is zero for

\(i+j > n+1\).

Arguments

x

A vector of real numbers. Grid points corresponding to the tabulated (known) values of the function.

f

A vector of real numbers. Tabulated (known) values of the function, corresponding to the grid x.

x0

A vector of real numbers. These are the grid points chosen for the interpolation. All points of this grid need to be within the tabulated grid.

Examples

# Tabulated values: f(x) = x^3-2*x^2+3*x-1
x <- c(0.1,0.4,0.6,0.8,0.9)
f <- x^3-2*x^2+3*x-1

# Interpolation point
x0 <- 0.75

# Upper-triangular matrix of N-A values
P <- nevaitpol(x,f,x0)

# From level 4 onward the interpolated value
# does not change because f(x) is a 3rd-degree polynomial
print(P)