VANDERCORPUT SEQUENCES, KAKUTANI TRANSFORMS AND ONE-DIMENSIONAL NUMERICAL-INTEGRATION

[摘要] It is shown that many functions can be empirically integrated with the Van der Corput sequences with an O(square-root ln n/n) or O(1/n) rate according to their smoothness (the first rate derives from a new Koksma-Hlawka-like inequality using the diaphony). Then we show that, as for the discrepancy estimates, these properties still hold when considering an extension of these sequences generated by ergodic transforms.

[发布日期] 1992-12-09

[关键词] NUMERICAL INTEGRATION;DISCREPANCY;DIAPHONY;ERGODIC THEORY