I: Numerical Methods

Question 1

Limitations of change of sign method

Answer 1

• If the function is not continuous, it does not work
• If the function has multiple roots between the limits, they are missed
• If the function has a root with no sign change (ie a repeated root), it is missed

Question 2

Staircase and cobweb diagrams

Answer 2

CURVE
LINE (y=x) <–>
up to the CURVE
across to the LINE
up to the CURVE
‘Crosses the line for pole position!!’

Question 3

Failure of x=g(x) method

Answer 3

• If gradient of curve is steeper than y=x, the root will not be found
• Unlikely to find all roots using this method
• The closer the gradient is to 1 or -1, the more iterations needed

Question 4

Failure of the Newton-Raphson method

Answer 4

• If substitution of denominator = 0, cannot divide by 0
• Might hone in on wrong root