Hessian Matrix
Numerically compute the Hessian matrix.
hessian(f, x0, h = .Machine$double.eps^(1/4), ...)
f |
univariate function of several variables. |
x0 |
point in R^n. |
h |
step size. |
... |
variables to be passed to |
Computes the hessian matrix based on the three-point central difference formula, expanded to two variables.
Assumes that the function has continuous partial derivatives.
An n-by-n matrix with \frac{\partial^2 f}{\partial x_i \partial x_j} as (i, j) entry.
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.
f <- function(x) cos(x[1] + x[2])
x0 <- c(0, 0)
hessian(f, x0)
f <- function(u) {
x <- u[1]; y <- u[2]; z <- u[3]
return(x^3 + y^2 + z^2 +12*x*y + 2*z)
}
x0 <- c(1,1,1)
hessian(f, x0)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.