Laplacian Operator

Numerically compute the Laplacian of a function.

laplacian(f, x0, h = .Machine$double.eps^(1/4), ...)

Arguments

f

univariate function of several variables.

x0

point in \(R^n\).

h

step size.

...

variables to be passed to f.

Details

Computes the Laplacian operator \(f_{x_1 x_1} + \ldots + f_{x_n x_n}\) based on the three-point central difference formula, expanded to this special case.

Assumes that the function has continuous partial derivatives.

Value

Real number.

References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

See also

hessian

Examples

f <- function(x) x[1]^2 + 2*x[1]*x[2] + x[2]^2
laplacian(f, c(1,1))
#> [1] 4