%0 Journal Article %1 citeulike:11681830 %A Cranley, R. %A Patterson, T. N. L. %D 1971 %J The Computer Journal %K 68t05-learning-and-adaptive-systems 65d32-quadrature-and-cubature-formulas 65d30-numerical-integration %N 2 %P 189--198 %R 10.1093/comjnl/14.2.189 %T On the Automatic Numerical Evaluation of Definite Integrals %U http://dx.doi.org/10.1093/comjnl/14.2.189 %V 14 %X A critical examination is made of adaptive subdivision as a means of reliably and efficiently performing the automatic evaluation of definite integrals. A model is set up which embodies the basic features of adaptive schemes. Circumstances are discussed under which adaptive schemes may inspire false confidence in the results produced. The efficiency of the method is seriously impaired by any attempts to overcome this difficulty. The conclusions have been illustrated by appropriate numerical examples.

@article{citeulike:11681830, abstract = {{A critical examination is made of adaptive subdivision as a means of reliably and efficiently performing the automatic evaluation of definite integrals. A model is set up which embodies the basic features of adaptive schemes. Circumstances are discussed under which adaptive schemes may inspire false confidence in the results produced. The efficiency of the method is seriously impaired by any attempts to overcome this difficulty. The conclusions have been illustrated by appropriate numerical examples.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Cranley, R. and Patterson, T. N. L.}, biburl = {https://www.bibsonomy.org/bibtex/20a0aaa342511604596f76774502c6073/gdmcbain}, citeulike-article-id = {11681830}, citeulike-attachment-1 = {cranley_71_automatic_851672.pdf; /pdf/user/gdmcbain/article/11681830/851672/cranley_71_automatic_851672.pdf; 5524093269bdb8debbb1cc34f25a7f57b76590e0}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/comjnl/14.2.189}, citeulike-linkout-1 = {http://comjnl.oxfordjournals.org/cgi/content/abstract/14/2/189}, comment = {cited by Engels (1980, p. 406)}, day = 1, doi = {10.1093/comjnl/14.2.189}, file = {cranley_71_automatic_851672.pdf}, interhash = {34ac8d8dc3902f650748103d145908e0}, intrahash = {0a0aaa342511604596f76774502c6073}, journal = {The Computer Journal}, keywords = {68t05-learning-and-adaptive-systems 65d32-quadrature-and-cubature-formulas 65d30-numerical-integration}, month = jan, number = 2, pages = {189--198}, posted-at = {2012-11-13 09:29:17}, priority = {0}, timestamp = {2019-04-29T03:29:52.000+0200}, title = {{On the Automatic Numerical Evaluation of Definite Integrals}}, url = {http://dx.doi.org/10.1093/comjnl/14.2.189}, volume = 14, year = 1971 }