NM Flashcards
(24 cards)
Why can the answer only be expressed to 6 dp
The values provided are only to 6dp
Why is the range of answers of numbers so large
Because there is subtraction of nearly equal numbers/denominators
Meaning of $
Allows the column to be fixed in subsequent calculations, will not be dragged down
What are the limitations of the model formed by newton forward or Lagrange
May have a cubic or quad with neg coefficients so suggests after some time will decrease and maybe less than 0
- if x tends to infinity, y tends to infinity
Why method will or will not work
May need a sign change, may need to straddle root
If they haven’t said ‘WITHOUT CALCULATION’
Then calculate the next most accurate iteration from the two given and found
Meaning of NUM!
Number is too large to be processed or spreadsheet unable to compute a value.
Calculation cannot be performed and so cannot be stored
ALWAYS when difference in our values or dp
It’s because there is a loss of significant figures or subtracting of nearly equal denom
Meaning of $$
So that the other values are also multiplied by the value in the $$,.
An absolute cell reference
If first order convergence is decreasing
Whatever the con is, it is greater con that 1st order
If second order con is increasing
It is slower than second order, is not 2nd order
Secant Ad and Dis
Ad:
- no derivative required
- faster than bisection or regular
Dis:
- requires two initial guesses
- not guaranteed to converge
- may fail if function values are equal
Newton Raphson Ad and Dis:
Ad:
- fast convergence (2)
- requires only one initial guess
- efficient for well behaved functions
Dis:
- requires derivative
- fails at zero inflection
- not suitable for discontinuous functions
- May diverge if initial guess is poor
Bisection Ad and Dis:
Ad:
- easy and simple to use
- always converges
Dis:
-slow convergence
Showing relative error won’t be the same…
It will be different as the order of operations is different and is a different calculation not a rearrangement of the equation
Computer is always…
Stores vales to a higher precision than displayed
Speed of convergence using values
If it is close to 1 - slow con
Close to 0 - fast con
If they have GIVEN Mn and Tn…
Use both to to find S2n because we get higher value
If value is 0
Loss of sf and accuracy but if questioning computer, comp is storing to higher value than displayed
If max chopping error
For pennies - .99
Anything else - 0.1 or 0.01
Write detailed conclusions
Mark scheme is pedantic
If they want to see iteration process
Do it for three calculated values
If asking for an estimate in chopping/rounding questions
Use average and expected error
If value of k is given É.g 0.35
Say it is faster than second order method (0.25) but slower than 4th order method (0.0625)
