Numerical Methods Flashcards
Three numerical methods:
Newton-Raphson, Iteration, Change of sign
Which situations do we need to watch out for when using change of sign method?
Function may not be continuous, multiple roots within interval
How to manipulate function for iterative formula?
Rearrange to make x the subject (can still have x in it).
What shapes can iterative formulae produce?
Staircase or cobweb
When drawing these lines, where does the shape hit first?
Formulae line.
How does Newton-Raphson work?
Using tangent lines to find more and more accurate approximations.
When will Newton-Raphson go wrong?
If starting x is at turning point because tangent is horizontal, picking a point close to turning point as convergence will be very slow.
What does graph of x^1/2 look like?
Top left of a circle, but with a non-zero y-intercept.
