NumericalAlgorithms.jl

CIcodecovGitHub license

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
  • Statistical Tests
    • Wald–Wolfowitz runs test

Next steps to do

  • Optimization
  • Differential Equations (ODEs)& Systems of diff. eqs.
  • Partial Differential Equations (PDEs)
  • Stochastic process & SDEs
  • ...
  • More comments & self-commenting code

Visual tests for RNGs

lfg1000

ranmar1000

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/.