逼近论与逼近实践

Hacker News 上怎么说

• jacobolus · 2015 年

  对这个话题感兴趣的朋友可以看看 Chebfun，http://www.chebfun.org 还有 Lloyd Trefethen 写的《Approximation Theory and Approximation Practice》（逼近理论与逼近实践），前 6 章可以在线阅读，http://www.chebfun.org/ATAP/ 这篇博文的作者其实完全可以用 Clenshaw 算法，正如他提到 Numerical… 推荐的那样

  Folks interested in this topic should look at Chebfun, http://www.chebfun.org Also at Lloyd Trefethen’s book Approximation Theory and Approximation Practice, of which the first 6 chapters are available online, http://www.chebfun.org/ATAP/ The author of this blog post might as well have used Clenshaw’s algorithm as he mentioned was suggested by Numerical…

• jacobolus · 2015 年

  ……重载它们以用于连续函数逼近。这让用户的代码非常干净易读，不过内部实现会变得相当复杂。另外还推荐 Trefethen 的书《Approximation Theory and Approximation Practice》，书中阐释了该库背后的数学思想。前 6 章可免费在线获取：http://www.chebfun.org/ATAP/

  …overload them to work on their continuous function approximations. This makes for very clean and readable code for their users, though the internals get pretty complex. Also recommended is Trefethen’s book Approximation Theory and Approximation Practice, which explains the mathematical ideas underlying the library. First 6 chapters are freely available online: http://www.chebfun.org/ATAP/

• gp7 · 2017 年

  这个页面直接把我 Chrome 标签页搞崩溃了！！无论如何，要是对这玩意儿感兴趣到都在看这篇评论了，那就应该去查查 Trefethen 写的《Approximation Theory and Approximation Practice》[0]，那真是一本极好的书，把切比雪夫多项式讲得透彻极了。不过你能从中学会的真正绝活，其实是通过在函数的根处取样……

  This page crashes my chrome tab!! Anyway, anyone interested enough in this to be reading this comment thread should go look up approximation theory and approximation practice by trefethen [0], which is a very very good book, that covers chebyshev polynomials in a very clear way. The real party trick you get out of it, though, is that by taking samples of functions at the roots…

• jacobolus · 2015 年

  ……多项式。当你做出正确的“全局”（也就是不仅限于单点）逼近时，像数值微分这样的操作会精确得多。另外也可以看看 Nick Trefethen 的书《Approximation Theory and Approximation Practice》，前 6 章在线可读：http://www.chebfun.org/ATAP/atap-first6chapters.pdf

  …polynomial. Operations like numerical differentiation are much more accurate when you make the right “global” (i.e. not just at one single point) approximation. Also check out Nick Trefethen’s book Approximation Theory and Approximation Practice, the first 6 chapters of which are available online: http://www.chebfun.org/ATAP/atap-first6chapters.pdf

• widdma · 2020 年

  好文章，感谢分享。对这个话题感兴趣的人，我强烈推荐 Trefethen 的《Approximation Theory and Approximation Practice》。通俗易懂、直观有趣，同时又涵盖了大量的技术细节。

  Nice article, thanks. For anyone interested in the topic, I highly recommend Trefethen's Approximation Theory and Approximation Practice. It's approachable, intuitive, and fun while still covering a lot of technical detail.

• fractionalhare · 2020 年

  ……平均情况相对误差。Remez 交换算法生成平均相对误差反而更差的多项式，这种情况并不少见。在 Trefethen 的《Approximation Theory and Approximation Practice》中也对这一点进行了相当深入的探讨。

  …average case relative error. It's not uncommon for the Remez exchange to produce polynomials which actually have worse average case relative error. This is also covered in considerable depth in Trefethen's Approximation Theory and Approximation Practice.

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