Good lattice points, discrepancy, and numerical integration

Clicks: 86
ID: 261206
1970
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Emerging

Ranked #42 of 70 articles by views in annali di matematica pura ed applicata

Most read Least read

Bar heights use a square-root scale.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Methods based on Diophantine approximations lead to a simple and easy construction of rational vectors the multiple of which, reduced modulo 1, form finite sequences of points with certain properties of equipartition over the unit square. Given a function of bounded variation over this square, it is suggested that computing the average of its values at the points of such a sequence can be a practical method of numerical integration. Precise bounds for the error ore obtained. In the general case, these are of the order of the product of the reciprocal and of the logarithm of the number of points; in the case of a function satisfying stated conditions of regularity and periodicity, they are of the order of the logarithm of the number of points divided by an appropriately high power of this number. A slight sharpening of some well-known results on equipartiton is obtained incidentally.
Reference Key
zaremba1970annaligood Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors S. K. Zaremba;S. K. Zaremba;
Journal annali di matematica pura ed applicata
Year 1970
DOI
doi:10.1007/BF02415091
URL
https://link.springer.com/article/10.1007/BF02415091
Keywords
mathematics general

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.