# Notes - Continuous Mathematics HT23, Error

### Flashcards

If you have a function $f(x)$ and a program that approximates the function as $\hat f(x)$, then what is the forward error for $x$?

When you have a function $f(x)$ and a program that approximates the function as $\hat f(x)$, then the forward error is

\[\hat f(x) - f(x)\]
Why is this rarely used in practice?

Because if you know the exact value of $f(x)$, you wouldn’t need to approximate it.

If you have a function $f(x)$ and a program that approximates the function as $\hat f(x)$, then what is the backward error for $x$?

when $\hat f(x) = f(\hat x)$.

Why **isn’t** floating point error a form of truncation error?

**isn’t**floating point error a form of truncation error?

Because truncation error specifically refers to cutting off some infinite process.

Suppose you approximate a function $f$ with it’s Taylor series $\hat f$. Then what is the form of error introduced here called?

Truncation error.

What’s the technical term for the class of errors that include errors involving floating point arithmetic?

Roundoff error.

What type of graph do you need to plot error against iteration steps in order to see straight lines for linear convergence, parabolas for quadratic, etc.?

- Error on log scale
- Iterations on linear scale

What does it mean for an iterative algorithm to converge quadratically?

where $C > 0$.