Q3: Choose one of the following two problems:

1

(a) Show that the following equality is true:

d²

dt2

m

A¹h(x(t)) = x(t)¹A₁V²h₂(x(t))

[EXX³h (@(0))] #

i=1

(t) + A¹Vh(x(t))ä(t)

[15 marks]

Where A Rmx1, h: Rnx1 → Rmx1, x R → Rx1 and t E R. The bold notation Vh

denotes the Jacobian matrix of h. This calculation is used in week 10 lectures notes (along

with some similar versions).

(b) Independently investigate non-linear least squares. Provide a concise derivation and con-

clude by showing that each iteration of the Gauss-Newton algorithm is equivalent to solving

a linear system.

[20 marks]