论文标题
tanh-sinh使用浮点算术的单一集成和多重整合的正交
Tanh-sinh quadrature for single and multiple integration using floating-point arithmetic
论文作者
论文摘要
在科学研究的所有领域，尤其是物理学领域，估计具有或没有终点奇异性的单维积分（具有或没有终点奇点）的问题。尽管已知Tanh-sinh Quadrature可以很好地处理大多数这些情况，但其使用并未在物理学家中广泛传播。此外，尽管大多数计算受到有限精确的浮点算术的限制，但对tanh-sinh正交的类似考虑的文献大多缺乏文献，在这些文献中通常会假定Infinite Precision Floating Point数字。同样，很少有关于将tanh-sinh正交在多个集成中应用的信息。 当使用tanh-sinh Quadrature进行单个和多重整合时，我们已经研究了与有限精确的浮点数相关的风险和局限性，同时获得了出色的收敛速率。此外，本文为使用限量精确的浮点数编号和避免数值不稳定性提供了简单实现的建议。
The problem of estimating single- and multi-dimensional integrals, with or without end-point singularities, is prevalent in all fields of scientific research, and in particular in physics. Although tanh-sinh quadrature is known to handle most of these cases excellently, its use is not widely spread among physicists. Moreover, while most calculations are limited by the use of finite-precision floating-point arithmetic, similar considerations for tanh-sinh quadrature are mostly lacking in literature, where infinite-precision floating-point numbers are often assumed. Also little information is available on the application of tanh-sinh quadrature to multiple integration. We have investigated the risks and limitations associated with limited-precision floating-point numbers when using tanh-sinh quadrature for both single and multiple integration, while obtaining excellent convergence rates. In addition, this paper provides recommendations for a straightforward implementation using limited-precision floating-point numbers and for avoiding numerical instabilities.
