• About me

• C#
• Java

• 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
• Eigenvalues of a random matrix
Computing Eigenvalues by the use of the characteristic polynomial

• 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

Machine learning and Artificial Intelligence

• MachineLearning and AI
PCA, Gradient descend, BackPropagation, max. log likelihood, Sequential minimal optimization

Digital signal processing

• Fourier transformations and digital filters
Discrete and fast Fourier transformations, Goertzel, Reinsch, Hartley and digital filters

Interpolation

• 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