Numerical Computation Flashcards
What does numerical computation refers to? Typical examples?
It refers to the set of algorithms aiming to estimate a solution through an iterative process rather than solving analytically. The process will “test” solutions until landing one that is close enough.
Typical examples are optimization (finding max or min of a function) and solving system of linear equation.
What is the main difficulty in performing continuous math on a digital computer?
You have to represent an infinite amount of numbers with a finite number of bytes.
How rounding error can be a problem? What are the two forms of it?
Rounding can be a problem as it can make processes that work in theory crash in practice. Underflow is rounding down a number to zero and it can cause errors in division by 0 for example. Overflow is number being replaced by +-inf.
What is conditioning, what is the condition number of a function?
The conditioning of a function refers to how much its output change when we slightly change its input. A poorly conditioned function will see its output change a lot when input change slightly, and will therefore amplify rounding errors coming as input. The condition number is the ratio between the biggest and the smallest eigenvalue, the higher it is the more unstable the calculations may be.
