Approximations Flashcards Preview

MATH2089 > Approximations > Flashcards

Flashcards in Approximations Deck (15)
Loading flashcards...
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

what can happen if we do arithmetic involving a large number and a comparably smaller number, and how can we alleviate this?

will cause catastrophic cancellation, can rearrange the expression with the catatropshic cncellation into a mathematically equivalent but numerically preferable expression