Study guide for Examlet 3

Here is a non-exhaustive list of questions you should be able to answer as you prepare for the examlet.

Past chapters

See the

(Recall from the course policies that our examlets are cumulative.)

As a hint, do make sure you're familiar with the 'distribution switch' formula for sampling, and make sure you know how to apply it.

What are absolute and relative errors?
What does it mean for a result to have $n$ accurate digits?
What are common sources of error in numerical methods?
How does the number of accurate digits relate to rounding?
What is a condition number? How would you approximate one given data on relative errors on inputs and outputs?

What is fixed point arithmetic? How are numbers represented in fixed point?
What is floating point arithmetic? How are numbers represented in floating point?
What is the significand? the exponent? of a floating point number
What is machine epsilon?
How can you quantify the least possible amount of rounding error that floating point arithmetic introduces with every operation?
How are floating point numbers stored? What is the 'implicit one' in the significand?
How is zero represented in floating point?
What are subnormal numbers? What is (gradual and non-gradual) underflow? overflow?
How is floating point addition performed?
What is catastrophic cancellation? How can you estimate the relative error (/number of digits) in the result of a calculation that incurs catastrophic cancellation?

How are images represented as vectors? What does addition/scalar multiplication mean for them?
How are sound clips represented as vectors? What does addition/scalar multiplication mean for them?
How are shapes represented as vectors? What does addition/scalar multiplication mean for them?
How do matrices operate on bases? How can linear operations on a basis be expressed using a basis?