DEPRECATED: I'm giving up with Julia and I'll implement similar algorithms in another language. If you want to develop further, please fork this repository.

Why I gave up with Julia:

1. Lack of OOP
2. Lack of static type checking: most errors were encountered in runtime
3. Unreadable library source codes (due to lack of OOP and type system)
4. ...

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NumericalAlgorithms.jl

Numerical algorithms implemented in Julia.

Installation

Install the package with add https://github.com/mrtkp9993/NumericalAlgorithms.jl in package mode (]).

Algorithms

Currently implemented:

• Root finding algorithms
  • Secant method
  • Broyden's method
• Differentation
  • Automatic differentiation via dual numbers
• Integration
  • Composite Simpson - One dim.
  • Double Simpson - Two dim.
  • Monte Carlo Integration - Arbitrary dimension
• Random Number Generators (RNGs)
  • Pseudo-random numbers
    • Lagged Fibonacci generator
    • RANMAR
  • Quasi-random numbers
    • van der Corput sequences
    • Halton sequences
    • Faure sequences
    • Sobol sequences
• Markov Chain Monte Carlo (MCMC) for sampling
• Statistical Tests
  • Wald–Wolfowitz runs test

License

Distributed under the GPL License. See LICENSE for more information.

Contact

Murat Koptur, LinkedIn

Email: muratkoptur@yandex.com

References

• Press, William H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes 3rd Edition: The Art of Scientific Computing (3rd ed.). Cambridge, England: Cambridge University Press.
• Kochenderfer, M. J., & Wheeler, T. A. (2019). Algorithms for Optimization (The MIT Press) (Illustrated ed.). The MIT Press.
• Burden, R. L., & Faires, D. J. (2010). Numerical Analysis (9th ed.). Cengage Learning.
• Zwillinger, D. (2018). CRC Standard Mathematical Tables and Formulas, 33rd Edition. Amsterdam University Press.
• Stoop, R., Hardy, A., Hardy, Y., & Steeb, W. (2004). Problems and Solutions in Scientific Computing with C++ and Java Simulations. World Scientific Publishing Company.
• Weinzierl, S. (2000, June 23). Introduction to Monte Carlo methods. ArXiv.Org. https://arxiv.org/abs/hep-ph/0006269.
• Lists of small primes. (2020). The PrimePages: Prime Number Research & Records. https://primes.utm.edu/lists/small/.