Table 1.

Numerical algorithm to solve the problem in Eq. (1)

Input: α, β, R0, T0 and a stopping criteria ϵ

Output: Y* and R*, T*

Procedure: Set t = 1;

1. Compute Yt by solving the problem in Eq. (4) using Eqs. (5) and (6);

2. Compute Rt and Tt by solving the problem in Eq. (7) using the Horn’s quaterion-based method;

3. If max (|Yt−Yt−1|/|Yt|) ≤ ∈, Y* = Yt, R* = Rt and T* = Tt; otherwise, set t = t + 1, go to Step 1.