Numerical methods library in C#

[Proektsoftbg]

Hello guys,

I created a new repository with numerical methods in C#:

https://github.com/Proektsoftbg/Numerical

I also includes comparative tests, that we used for the methods that we have developed for Calcpad:

https://github.com/Proektsoftbg/Numerical/tree/main/Numerical.Benchmark/doc

About root finding, the method in Calcpad (modAB) outperforms all other methods with 16 iterations per function average:
https://github.com/Proektsoftbg/Numerical/blob/main/Numerical.Benchmark/doc/Root/Root-test-results.pdf

The test functions are presented here:
https://github.com/Proektsoftbg/Numerical/blob/main/Numerical.Benchmark/doc/Root/Root-test-functions.pdf

About numerical integration, Gauss-Lobatto quadrature is the most effective one that works for both continuous and non-continuous functions. It is currently implemented in Calcpad. However, I wonder whether to include TanhSinh as an alternative ($Integrate command). It has outstanding performance for continuous functions, but fail for non-continuous.

What is your oppinion?

[hildebrandopsj]

I Will read carefully this material. My question is, why not both?

[Proektsoftbg]

That is exactly the idea! "Alternative" means "both":

$Area{f(x) @ x = a : b} will remain as is with Gauss-Lobatto integration.
$Integrate{f(x) @ x = a : b} will perform TanhSinh Integration, but only for continuous functions.

We can also make $Integrate to work with infinite boundaries and automatically switch to Exp-Sinh or Sinh-Sinh quadratures depending on the specified boudaries.

https://ems.press/content/serial-article-files/2719

[Proektsoftbg]

OK, I added the $Integrate command. It also formats the expression with the integral symbol. Formatting of sums and products has also been improved. Now, they are displayed exactly "by the book":