Rounding Errors in Romberg Algorithm

Janusz Chojnacki, and Andrzej Kiełbasiński. "Rounding Errors in Romberg Algorithm." Mathematica Applicanda 15.29 (1987): null. <http://eudml.org/doc/292956>.

@article{JanuszChojnacki1987,
abstract = {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 Romberg extrapolation on the cumulation of rounding errors is bounded by a constant.},
author = {Janusz Chojnacki, Andrzej Kiełbasiński},
journal = {Mathematica Applicanda},
keywords = {Roundoff error},
language = {eng},
number = {29},
pages = {null},
title = {Rounding Errors in Romberg Algorithm},
url = {http://eudml.org/doc/292956},
volume = {15},
year = {1987},
}

TY - JOUR
AU - Janusz Chojnacki
AU - Andrzej Kiełbasiński
TI - Rounding Errors in Romberg Algorithm
JO - Mathematica Applicanda
PY - 1987
VL - 15
IS - 29
SP - null
AB - 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 Romberg extrapolation on the cumulation of rounding errors is bounded by a constant.
LA - eng
KW - Roundoff error
UR - http://eudml.org/doc/292956
ER -