Numerical methods cheatsheet

numerical_methods.md

Finding Roots of Polynomials and Functions

i.e., solving nonlinear equations.

• In general
• Newton–Raphson method
• Steffensen's method
• Muller's method

Methods for solving systems of linear equations:

• Gauss elimination
• LU decomposition, Crout's algorithm
• Cholesky decomposition
• Jacobi method
• Gauss–Seidel method

The Newton method may be generalised to solve systems of nonlinear equations as well. Another approach is the class of iterative methods based on relaxation.

Methods for finding the roots of polynomials:

• Sturm's theorem
• Bairstow's method

Optimisation

• In general (navbox)
• Newton's method
• Gradient descent
• Nelder–Mead method
• BFGS and L-BFGS
• Conjugate gradient method
• Golden-section search
• Brent's method
• Simulated annealing

Integration

• In general
• Methods based on interpolation
• Monte Carlo methods

See also the next section.

Solving ODEs

• In general (navbox)
• Euler metohd
• Runge–Kutta methods
• Linear multistep methods (Adams–Bashforth, Adams–Moulton)