Day 9, Tues, Feb 27, 2018

Quiz #4

On Numpy

Mayfly population model: additional ideas

Quantifying the exponential separation (or convergence)

Estimate average slope

Grapical iteration for understanding dynamics

Questions?

Floating-point number representation and arithmetic

We've been using a representation of the real numbers without knowing or thinking much about it.

A sensible scheme for computing in the real numbers (as opposed to integers)?

Rationals are dense in the reals: how about mayfly model in exact arithmetic?

Approximate representation in 64 bits

how big?

how distributed?

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

Exercise: plot ((1+x)-1)/x on remedies