……方程。要是你搞砸了，离散化带来的非物理人工痕迹就会毁掉你的计算。取决于你具体的实现方式，舍入误差可能会变好也可能会更糟，Foreman Acton 的《Numerical Methods that Work》以及后来的《Real Computing Made Real》揭示了控制这些误差的技术，让你用 float 就能搞定很多事，而且有人还会指出，换成 double 其实也给你留不出多少余量……
…equations. If you did it wrong, unphysical artifacts of the discretization would wreck your calculation. Depending on how you did things rounding errors can be made better or worse, Foreman Action's Numerical Methods that Work and later Real Computing Made Real reveal techniques for managing these errors that let you accomplish a lot with floats and some would point out that going to doubles doesn't win you that much slack…
手算可以得到精确解，在某些场景下这可能更合适。Forman Acton 在其经典名作《Numerical Methods That Work》中，就用一元二次方程公式作为例子，展示了计算机如何能给出一个荒唐至极的错误解答。
Solving it by hand gives an exact answer, which in some contexts, might be preferable. Forman Acton, in his classic book, Numerical Methods That Work, uses the quadratic formula as an example to illustrate how a computer can give a wildly incorrect solution.
……写出由于舍入和数值不稳定性而导致行为异常的数值计算代码。Foreman Acton 之所以写了本叫《Numerical Methods that (usually) Work》的书是有原因的。https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/... 用 C、Haskell、OCaml 或 CUDA 随手写点东西，你就彻底错过了人们在 1970 年代的 FORTRAN 代码里积累了 40 多年的经验。
…write numeric codes that do the wrong thing with rounding and numerical instability. There's a reason why Foreman Acton wrote a book titled Numerical methods that (usually) work. https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/... Code something up in C, Haskell, oCAML or CUDA and you miss out on the 40+ years of experience people have had with a FORTRAN code from the 1970s.
……在我们拥有横跨大西洋的通用网络之前，就已经知道怎么通过电子邮件从 Netlib 获取代码了。我发现 Nick Higham 对我们当年的本科教材情有独钟——那是更早时期的书，Acton 的《Numerical Methods that Work》。
…knew how to get code from Netlib by email before we had general trans-Atlantic network access. I found Nick Higham has a soft spot for the undergraduate textbook we had, from rather earlier, Acton's Numerical Methods that Work.
……方程。要是你搞砸了，离散化带来的非物理人工痕迹就会毁掉你的计算。取决于你具体的实现方式，舍入误差可能会变好也可能会更糟，Foreman Acton 的《Numerical Methods that Work》以及后来的《Real Computing Made Real》揭示了控制这些误差的技术，让你用 float 就能搞定很多事，而且有人还会指出，换成 double 其实也给你留不出多少余量……
…equations. If you did it wrong, unphysical artifacts of the discretization would wreck your calculation. Depending on how you did things rounding errors can be made better or worse, Foreman Action's Numerical Methods that Work and later Real Computing Made Real reveal techniques for managing these errors that let you accomplish a lot with floats and some would point out that going to doubles doesn't win you that much slack…
手算可以得到精确解，在某些场景下这可能更合适。Forman Acton 在其经典名作《Numerical Methods That Work》中，就用一元二次方程公式作为例子，展示了计算机如何能给出一个荒唐至极的错误解答。
Solving it by hand gives an exact answer, which in some contexts, might be preferable. Forman Acton, in his classic book, Numerical Methods That Work, uses the quadratic formula as an example to illustrate how a computer can give a wildly incorrect solution.
……写出由于舍入和数值不稳定性而导致行为异常的数值计算代码。Foreman Acton 之所以写了本叫《Numerical Methods that (usually) Work》的书是有原因的。https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/... 用 C、Haskell、OCaml 或 CUDA 随手写点东西，你就彻底错过了人们在 1970 年代的 FORTRAN 代码里积累了 40 多年的经验。
…write numeric codes that do the wrong thing with rounding and numerical instability. There's a reason why Foreman Acton wrote a book titled Numerical methods that (usually) work. https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/... Code something up in C, Haskell, oCAML or CUDA and you miss out on the 40+ years of experience people have had with a FORTRAN code from the 1970s.
……在我们拥有横跨大西洋的通用网络之前，就已经知道怎么通过电子邮件从 Netlib 获取代码了。我发现 Nick Higham 对我们当年的本科教材情有独钟——那是更早时期的书，Acton 的《Numerical Methods that Work》。
…knew how to get code from Netlib by email before we had general trans-Atlantic network access. I found Nick Higham has a soft spot for the undergraduate textbook we had, from rather earlier, Acton's Numerical Methods that Work.