related: there is a short series of exercises in SICP that explore the idea of building an interval arithmetic library. i.e. numerical values are represented by intervals [a, b] which encode their uncertainty/error:
Exercise 2.14 and onwards point out that two expressions that are algebraically equivalent for perfectly accurate values stop being equivalent once we introduce uncertainty. This is only for a toy example expression with 2 variables. Suppose we want to solve a linear system of equations in 100s of thousands of variables. Is it tractable to track the uncertainty for all of those variables at once? Will their uncertainties be dependent? ...
Comments
related: there is a short series of exercises in SICP that explore the idea of building an interval arithmetic library. i.e. numerical values are represented by intervals [a, b] which encode their uncertainty/error:
http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html...
Exercise 2.14 and onwards point out that two expressions that are algebraically equivalent for perfectly accurate values stop being equivalent once we introduce uncertainty. This is only for a toy example expression with 2 variables. Suppose we want to solve a linear system of equations in 100s of thousands of variables. Is it tractable to track the uncertainty for all of those variables at once? Will their uncertainties be dependent? ...
aye, this matches my intuition: having a lower bound and an upper bound (as rational numbers) on each value means you can:
- go back and improve if necessary, or otherwise - express the uncertainty of a comparison
thanks for the link :)
... that is a really good idea. Why do I keep putting off reading that book?!