Day 10, Thursday, Mar 1, 2018

Quiz #4.5

Binary representation of numbers

Subplots

better code

Floating point representation and arithmetic

IEEE 754 floating point standard

sign, exponent, mantissa

machine epsilon, min, max

toy system, toy system with denormalization

Floating point arithmetic

catastrophic loss of significance

Example 1

Exercise: plot ((1+x)-1)/x on [-2e15,2e15]

Exercise: plot log(1+x)/x

Example 2

roots of a quadratic

Remedies

reformulation as equivalent expression

approximation can be better than exact!

Fitting a model to data

Example: approximately exponential separation of trajectories in mayfly model

How to define and calculate the "best" straight line?