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The article discusses an algorithm for Fourier cosine integral (FRCOS). The user should keep in mind that an adaptive approach does not guarantee that the final answer has an error less than ET, which specifies the required absolute accuracy, accidental false convergence is always a possibility. While empirical evidence suggests that FRCOS is relatively immune to this, some examples of false convergence were encountered during the test of the algorithm. The user should always try to safeguard against this possibility, for example by making ET smaller than required, or by doing the computations twice with different values of ET and HL which represents an upper limit on the stepsize.

The article presents information on a multidimensional Monte Carlo quadrature with adaptive stratified sampling. This procedure evaluates the n-dimensional integral by the Monte Carlo method. In the procedure, a set of samples is taken uniformly stratified throughout the entire volume. Based on the variance in these samples, a decision is made as to whether more samples are needed. If more samples are needed, the volume is cut in half and the entire procedure is repeated on each half, the halvings being repeated as required. The choice for axis for the halving is based on samples of the gradient. The result of this process is that the overall stratification is not uniform, but approaches optimum as more and more samples are taken, since more halvings are taken in the regions of high variance.