List of Algorithms

Candidate algorithms for the topics under CLO 1: Numerical Methods. Each is tagged with how important it is that the course cover it.

Linear Algebraic Equations

• Gaussian elimination [Essential]
• LU decomposition [Essential]
• Cramer’s rule (as an example of a “bad” algorithm with exponential complexity) [Somewhat Desirable]

Nonlinear Algebraic Equations

• Bracketing methods (e.g. bisection) [Essential]
• Fixed-point iteration [Essential]
• Newton’s method [Essential]
• Muller’s method [Somewhat Desirable]

Ordinary Differential Equations (ODEs)

• Euler’s method [Essential]
• Runge-Kutta methods [Essential]
• Adaptive Runge-Kutta (Runge-Kutta-Fehlberg) [Highly Desirable]
• Multistep methods [Somewhat Desirable]
• Shooting method for boundary-value problems [Highly Desirable]
• Finite difference method for boundary-value problems [Highly Desirable]

Numerical Optimization

• Fixed step size gradient descent [Essential]
• Descent with line search [Highly Desirable]
• Newton’s method [Highly Desirable]
• Quasi-Newton, conjugate gradient, etc. [Somewhat Desirable]
• Momentum, Adam, etc. [Highly Desirable]

Regression

• Linear least squares with linear basis functions [Essential]
• Linear least squares with nonlinear basis functions [Highly Desirable]
• Nonlinear regression [Highly Desirable]
• Neural network regression [Highly Desirable]