content

• Preface
• Orthogonal Transformation and Least Squares
• Cholesky Decomposition
• The Square Root Free Cholesky Algorithm
• The Householder Transformation
• Modified Gram–Schmidt orthogonalization
• Solving nolinear Equation
• Newton-Raphson Method
• mulit-root iterative improvement
• Muhammad method
• numerical Optimization
• Successive parabolic interpolation
• Newton’s Method
• Quasi-Newton Methods(DFP)
• Quasi-Newton Methods(BFGS)
• Interpolation
• Lagrange interpolation
• Newton method
• Hermit interpolation
• data fitting
• Polynomial fitting ephemeris
• Chebyshev fitting ephemeris
• ODE
• Symplectic Geometric Algorithms for Hamiltonian Systems
• Precise integration method
• Appendix：Matrix and Linear algebra class design
• C++ matrix class design
• C# matrix class design
• golang's slice for linear algebra

preface

In engineering calculations and data processing, various numerical algorithms are often involved. For the convenience of beginners, this website provides some commonly used numerical methods. The algorithms here are generally "textbook" algorithms and have not been optimized for engineering. I am not responsible for any project losses caused by the use of the code on this website. All algorithms on this website have been verified and compared with scientific software such as MATLAB.

The code mainly consists of some programs written in recent years, so the programming languages are not unified. The provided code mainly includes: Java, C#, Fortran, MATLAB, C++, Golang, Python, and several other languages. Among them, languages such as C#, C++, and Golang define matrix classes, so the code looks like "pseudo-code". The design methods of matrix and linear algebra classes are described in the appendix.

Mathematical formulas need to be written in LaTeX, which is time-consuming, so some statements are written briefly. If you have any questions or other suggestions, please feel free to contact me via email: song.yz@foxmail.com. WeChat: math-box.