Numerical methods

Numerical methods refer to a broad field of mathematics focused on finding approximate solutions via an iterative update of estimates, instead of analytically/symbolically finding the exact correct solution.

This is useful because we often must find solutions for many problems on computers, which work best in an iterative way.

Implications

Computers are only able to store a subset of the real numbers. This means that we must incur some approximation error when performing computations. If our algorithms don’t minimise the accumulation of rounding errors, they could fail.

Underflow is when numbers near 0 are rounded to 0. Overflow is when we approximate large numbers with $\pm \infty$.

Sub-pages

• Optimisation applications
  • Gradient descent
• Calculus and ODEs
  • Numerical integration
  • Runge-Kutta methods
    • Euler’s method