Flashcards in Approximations Deck (15)
what is a flop?
Floating Point OPERATION
What is a flop per second?
a unit of measurement used to approximate the time it takes for an operation to be executed
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)
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
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.
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
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
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
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
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)
whats the formula for the relative error of x1?
what gives an estimate for the relative error?
epsilon * abs(x) , where epsilon is the relative precision on a computer
what is a rounding error?
refers to the error associated with rounding a value to n number of sig figs
what is confidence?
the no. of sig figs we can accuately say that the value of something is