Scientific Computing Algorithms

This is a collection of algorithms related to various scientific computing applications.

The algorithms are written in MATLAB and can be loaded into MATLAB and used.

Algorithm Description

Rather than trying to explain each algorithm, I will just link relavent literature that explains them better than I could.

Decomposition

• Cholesky Decomposition (cholesky.m)
  https://en.wikipedia.org/wiki/Cholesky_decomposition

• L-U Decomposition (lu_decomp.m)
  https://en.wikipedia.org/wiki/LU_decomposition

• Q-R Decomposition (qr_decomp.m)
  https://en.wikipedia.org/wiki/QR_decomposition

• Singular Value Decomposition (sv_decomp.m)
  https://en.wikipedia.org/wiki/Singular_value_decomposition

Iterative Methods

• Jacobi Method (jacobi.m)
  https://en.wikipedia.org/wiki/Jacobi_method

• Gauss-Seidel Method (gauss_seidel.m)
  https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method

• SOR, Successive Over Relaxation, Method (sor.m)
  https://en.wikipedia.org/wiki/Successive_over-relaxation

Gradient Methods

• Gradient Descent Method, Steepest Descent (gradient_sd.m)
  https://en.wikipedia.org/wiki/Gradient_descent

• Conjugate Gradient Method (conj_gradient.m)
  https://en.wikipedia.org/wiki/Conjugate_gradient_method

Solving Triangular Systems

• Upper Triangular System (upper_tri.m)
  Simple algorithm to solve an upper triangular system

• Lower Triangular System (lower_tri.m)
  Simple algorithm to solve a lower triangular system