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RedditI want to share some (in my opinion) interesting algorithms I’m working with and try to explain the Math behind them as detailed as possible as there are many explanations around in the net that one cannot understand because they are unclear or missing parts (my experience
)- General maths Basic Matrix calculations, complex numbers, trigonometry, differential calculus, Taylor polynomials
- Elimination algorithm by Gauss
- Rotation Matrix
- Inverse Matrix, Cramers method, cofactor matrixes
- LU decomposition LU decomposition by Crout and by using Frobenius matrixes with row switching
- Cholesky decomposition
- Householder transformation
- Singular value decomposition
- Gram-Schmidt QR decomposition One more way to solve a matrix equation
- Quadratic equation To solve a quadratic equation
- Cubic equation by Cardano To solve a cubic equation
- Real roots of polynomials by Newton/Maehly To find real roots of polynomials
- Complex roots of polynomials by Bairstow To find complex roots of polynomials
- Roots of polynomials by the calculation of eigenvalues To compute complex and real roots of polynomials by the QR decomposition
- Partial fraction decomposition Partial fraction decomposition of a truly broken rational function
- Eigenvalues basically Use of the characteristic polynomial
- Eigenvalues Vector iteration Vector iteration and inverse Vector iteration
- Eigenvalues of symmetric matrixes Jakobi transformation
- Eigenvalues of a random matrix QR decomposition
- Classic Linear regression The classic Linear Regression how it is done in my poket calculator
- Equalization calculus Equalization calculus for polynomials using the method of the least squares, Cholesky decomposation or orthogonal transformations
- Equalization calculus SVD Equalization calculus for polynomials using the singular value decomposition
- Method of the least squares multi-dimensional Equalization calculus for more that 2 dimensional spaces
- Fourier transformations and digital filters Discrete and fast Fourier transformations, Goertzel, Reinsch and digital filters
- Polynomial interpolation
- Newton interpolation
- Newton Gregory interpolation Forward and backward interpolation by Newton Gregory
- Lagrange interpolation
- Neville interpolation
- Hermitian interpolation
- Chebychev polynomials Approximation and interpolation by the use of Chebychev polynomials
- Natural Splines Using Gaussian elimination algorithm or a LU decomposition
- Periodic Splines Using Gaussian elimination algorithm or a Cholesky decomposition
- End slope splines Cubic splines with defined start and end angle
- Bézier Splines
Integration and differentiation
- Differential calculus Numerical integration by Simpson, Romberg, Newton-Cotes, Legendre and Chebychev polynomials and Differential equation by Runge Kutta and Adams methods and Runge Kutta with addaptive step size.
Digital image processing
- Digital image filters Smoothing, sharpening and egde detection on digital images.
Some Java script
- Online solver I had to practice some Java script and so some online solvers were born
Just playing around
- Computing Pi by Archimedes and Newton's algorithm Pi with 1000 decimal places
- Computing a random root of a number
- To solve a Sudoku A recursive approach to solve a Sudoku
- To create a vintage style, oval shaped image Some digital image processing
- Andy Warhol emulator Some more digital image processing
- Plotting the Mandelbrot set The beauty of Mathematics