## Corner Peak Integrand Family

### Description:

*Dimensions: d*

The Corner Peak family of functions is quickly integrated analytically, to high precision. In its two-dimensional form, as shown in the plot above, the function is characterized by a flat surface which rises in a sharp peak at one corner of the integration region.

The d uneffective u-parameters are chosen randomly from [0, 1], and their values don't significantly affect the difficulty of integration.

Larger values of the d affective a-parameters result in a more prominent corner peak, thus resulting in more difficult integration.

The above two-dimensional plot is created using

**u**= (0.5, 0.5) and

**a**= (5, 5).

### Input Domain:

The function is integrated over x_{i}∈ [0, 1], for all i = 1, …, d.

### Code:

### Reference:

Genz, A. (1984, September). Testing multidimensional integration routines. In *Proc. of international conference on Tools, methods and languages for scientific and engineering computation* (pp. 81-94). Elsevier North-Holland, Inc..

For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.

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