Flashcards in Approximations Deck (15)
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1
what is a flop?
Floating Point OPERATION
2
What is a flop per second?
a unit of measurement used to approximate the time it takes for an operation to be executed
3
how do computers display n on integers?
they have to display floating points using a string of binary digits.
- the first binary digit stores the sign of the number: 0 if positive, 1 if negative
-the proceeding string of binary digits stores the value of the exponent; 2^(N-M), where N represents the number represented by the string of digits, and M=2^(N-1)-1
-the last string of digits stores the value of the mantissa(multiplying factor)
4
how do you find the actual floating point value?
multiply the exponent and the mantissa, using the sign from the first digit to determine the sign of the number
5
What do O(n^k) and o(n^k) represent?
they represent the Big O and Little O of a certain function - the value of k depending on whether n approaches zero or infinity.
6
What does k present for the Big O function when n goes to infinity?
for the Big O notation, limit as n goes to infinity of F(n)/n^k = constant, so k represents the power of n that dominates the function
7
What does k present for the Little O function when n goes to infinity?
limit as n goes to infinity of f(n)/n^k = 0
so k presents the smaller integer greater than the power of n that domminates the function
8
What does k present for the Big O function when n goes to zero?
k presents the power of n that least dominates the function
9
What does k present for the Little O function when n goes to zero?
k represents the greatest integer smaller than the power of n that least dominates the function
10
suppose that x, is the computed approximation of Xo, what is the absolute error of x?
would be given by AE(X1)=abs(X1-Xo)
11
whats the formula for the relative error of x1?
RE(x1)=abs(x1-xo)/abs(xo)
12
what gives an estimate for the relative error?
epsilon * abs(x) , where epsilon is the relative precision on a computer
13
what is a rounding error?
refers to the error associated with rounding a value to n number of sig figs
14
what is confidence?
the no. of sig figs we can accuately say that the value of something is
15