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Welcome to the numerical-veliz wiki!

These programs are examples for Numerical Analysis tutorial videos created by Oscar Veliz https://www.youtube.com/OscarVeliz. They are written in numerous languages such as C, Python, Haskell, SML/NJ, Julia, Ada, Rust, OCaml, Go, Kotlin, Perl, gnuplot, CLISP, Pascal, GNU Octave, and R. This accomplishes two tasks. The first to is to demonstrate that you can do Numerical Analysis in any language; that once you've learned one language you can program in anything. The second is to allow educators to use these programs as teaching tools without doing their students' homework for them. They are non-trivial, functional, and extensible pedagogical materials. The topics so far include:

Root-Finding

• Bisection Method
• False Position Method - Regula Falsi
• Fixed Point Iteration
• Aitken's Δ² Method
• Steffensen's Method
• Wegstein's Method
• Newton's Method
• Newton's Method Convergence Interval
• Horner's Method
• Laguerre's Method
• Halley's Method
• Householder's Method
• Secant Method
• Inverse Quadratic Interpolation
• Muller's Method

Fractals and Complex Plane

• Complex Plots
• Newton Fractal
• Halley Fractal
• Householder Fractal
• Laguerre Fractal
• Jarratt SPI Fractal

Hybrid Root-Finding

• Dekker's Method
• Brent's Method
• Newt-Safe

Eigenvalues

• Power Method
• Inverse Power Method
• Rayleigh Quotient

Systems of Equations

• Fixed Point Iteration for Nonlinear Systems
• Generalized Aitken-Steffensen
• Durand-Kerner Method
• Aberth-Ehrlich

Minimization

• Ternary Search
• Dichotomous Search
• Fibonacci Search
• Golden-section Search
• Jarratt's Method / Successive Parabolic Interpolation
• Brent's Minimization Method

Series

• Taylor Series
• Machin-like formula for π