Rounding Errors in Romberg Algorithm
It is shown that each quadrature computed by Romberg algorithm is exact for slightly perturbed data (computed values of the integrand). For the ordinary summation algorithm the cumulation of rounding errors is proportional to N, the number of quadrature modes. For more elaborate summation the cumulation is proportional to log N. For the binary floating point arithmetic with proper rounding of the sum, the cumulation of errors can be made practically independent of N. In each case the influence of...