trefethen function

Trefethen and Wagon Test Functions

Test functions for global optimization posed for the SIAM 100-digit challenge in 2002 by Nick Trefethen, Oxford University, UK.

fnTrefethen(p2)
fnWagon(p3)

Arguments

• p2: Numerical vector of length 2.
• p3: Numerical vector of length 3.

Details

These are highly nonlinear and oscillating functions in two and three dimensions with thousands of local mimima inside the unit square resp. cube (i.e., [-1, 1] x [-1, 1] or [-1, 1] x [-1, 1] x [-1, 1]).

Returns

Function value is a single real number.

References

F. Bornemann, D. Laurie, S. Wagon, and J. Waldvogel (2004). The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. Society for Industrial and Applied Mathematics.

Author(s)

HwB hwborchers@googlemail.com

Examples

x <- 2*runif(5) - 1
  fnTrefethen(x)
  fnWagon(x)

  ## Not run:

  T <- matrix(NA, nrow=1001, ncol=1001)
  for (i in 1:1001) {
    for (j in 1:1001) {
        T[i, j] <- fnTrefethen(c(x[i], y[j]))
    }
  }
  image(x, y, T)
  contour(x, y, T, add=TRUE)
## End(Not run)