我需要的是：绘图创建、插值的东西、计数的东西，例如
和
其中 L(x) 是根据原始已知函数 f(x) 生成的一些数据（点）构建的插值。这意味着我们知道原始函数。我们有一个已知的范围 (-a, a)。我们需要库来帮助我们计算范围内的数据点。我们需要使用该范围内的数据计算 L(x) 多项式。
我需要这个库是免费和开源的
What I need is: plots creation, stuff for interpolation, stuff for counting such things as
and
where L(x) is an interpolation built from some data (points) generated from original known function f(x). meaning we know original function. we have a range (-a, a) - known. We need library to help us calculate data points in range. we need to calculate L(x) a polinom using that data in that range.
I need this library to be free and opensource
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也许 Math.NET 可以帮助您。
Perhaps Math.NET can help you.
检查其他答案https://stackoverflow.com/questions/1387430/recommished-math- Library-for-c-net，特别是有几个人认为 MathDotNet 很好。
Check this other answer https://stackoverflow.com/questions/1387430/recommended-math-library-for-c-net, in particular several people think that MathDotNet is nice.
对于绘图创建，您可能需要 excel 互操作（为什么不？），或 ILNumerics.NET。
但我不明白其他要求。您想测量您不知道的函数的插值误差（在最大和 L1 范数中）？这不是一个编程问题，这是一个数学问题。
我建议您查看插值库（例如 Math.NET 包含一个，但许多其他库也这样做），看看它们是否提供“误差估计”之类的功能。
否则，您需要一本数学书，它将向您解释您需要估计插值误差的
f假设。这取决于你对f的规律性和插值方法的了解。编辑，有关提供的其他信息：有插值误差的封闭形式公式（这里作为起点）。但是任何数值积分例程（Math.NET 不提供）都会得到您想要的结果。看看其他人指出的库，此链接 将帮助您开始。
由于您似乎有常规函数（因为您进行多项式插值），所以我会使用简单的 Romberg集成，如果您找不到适合您需要的库（我对此表示怀疑），那么实现起来非常简单。请参阅 Numerical Recipes，第 3 版以获取示例代码。
For plot creation, you may want excel interop (why not ?), or ILNumerics.NET.
But I don't understand the other requirements. You want to measure interpolation errors (in the max and L1 norm) from a function you don't know ? This is not a programming question, it is a math question.
I suggest you look at interpolation libraries (Math.NET contains one for instance, but many others also do) and see if they provide such things as "error estimation".
Otherwise, what you need is a math book which will explain you the assumptions on
fthat you need to estimate the interpolation error. It depends on what you know about the regularity offand the interpolation method.Edit, regarding additional information provided: There are closed form formulas for interpolation errors (here as a starting point). But any numerical integration routine (which Math.NET does not provide) will get what you want. Have a look at libraries other people pointed out, this link will get you started.
Since you seem to have regular functions (since you do polynomial interpolation), I'd go with simple Romberg integration, which is quite simple to implement in case you don't find a library that suits your need (I doubt it). Have a look at Numerical Recipes, 3rd edition for sample code.
使用 Mathematica 怎么样？
What about using Mathematica?
Math.NET 和 ILNumerics.Net 都是开源的，都可以解您的方程。
Math.NET and ILNumerics.Net are both open source and will both solve your equations.