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