Numerical Methods

• The goal is to solve continuous problems using numeric approximation.

• Applying the methods of Numerical Methods requires knowledge on binary and computer number formats. Note that imprecisions due to how numbers are stored can cascade to inaccuracies when using numerical methods.

• The Machine Precision is defined as the gap between and the next floating point number. We denote this with .

• The approximation error is defined as the error between the true value and the computed value. We compute it as

  Where is our approximation and is the true value.

• The order of an iterative approximation method is a number such that the approximation error at the -th step follows the relation

  Where is a constant.

Topics §

• Root Finding Algorithms
• Numerical Differential Calculus
• Numerical Integral Calculus
• Numerical Optimization
• Numerical Linear Algebra
• Numerical Differential Equations

Calculus §

• Complicated Functions can be modeled from simpler pieces. For example using either a Taylor Series or a Maclaurin Series

Links §

• Numerical Methods — An Inquiry Based Approach with Python by Sullivan