Table 2.

Calculated Values for Numerical Example using Formulas from Table 1 (x_n+1 = (−2.0, 3.0, 1.0))

Formula 1	k = 3	α3 = (−0.59, −0.75, −0.29)
Principal	k = 2	α2 = (0.04, −0.40, 0.92)
Components	k = 1	α1 = (0.80, −0.53, −0.27)
Formula 2
Scores	k = 3	${\left(X^3\right)}^T=\left[\begin{array}{cccccccccc}\hfill -1.17& \hfill 0.53& \hfill -1.02& \hfill 1.12& \hfill 2.08& \hfill -1.61& \hfill 1.17& \hfill 2.00& \hfill 3.00& \hfill 3.00\\ \hfill 1.20& \hfill 0.24& \hfill 0.40& \hfill 1.36& \hfill -1.82& \hfill 0.53& \hfill -1.52& \hfill -1.03& \hfill -2.00& \hfill 3.00\\ \hfill -0.30& \hfill -1.00& \hfill 1.11& \hfill -1.69& \hfill .-0.76& \hfill 0.99& \hfill 0.71& \hfill -1.44& \hfill -1.00& \hfill 3.00\end{array}\right]$
	k = 2	${\left(X^2\right)}^T=\left[\begin{array}{cccccccccc}\hfill -1.58& \hfill 0.38& \hfill -0.97& \hfill 0.92& \hfill 2.43& \hfill -1.77& \hfill 1.70& \hfill 2.13& \hfill 3.54& \hfill 4.73\\ \hfill 0.24& \hfill 1.07& \hfill -1.21& \hfill 1.82& \hfill 0.92& \hfill -1.13& \hfill -0.66& \hfill 1.61& \hfill 1.22& \hfill -2.91\end{array}\right]$
	k = 1	${\left(X^1\right)}^T=\left[\begin{array}{cccccccccc}\hfill -1.67& \hfill 0.40& \hfill -1.03& \hfill 0.98& \hfill 2.57& \hfill -1.87& \hfill 1.80& \hfill 2.25& \hfill 3.74& \hfill 5.00\end{array}\right]$
Formula 3
Projections	k = 3	$\left[\begin{array}{cccccccccc}\hfill -1.17& \hfill 0.53& \hfill -1.02& \hfill 1.12& \hfill 2.08& \hfill -1.61& \hfill 1.17& \hfill 2.00& \hfill 3.00& \hfill 3.00\\ \hfill 1.20& \hfill 0.24& \hfill 0.40& \hfill 1.36& \hfill -1.82& \hfill 0.53& \hfill -1.52& \hfill -1.03& \hfill -2.00& \hfill 3.00\\ \hfill -0.30& \hfill -1.00& \hfill 1.11& \hfill -1.69& \hfill -0.76& \hfill 0.99& \hfill 0.71& \hfill -1.44& \hfill -1.00& \hfill 3.00\end{array}\right]$
	k = 2	$\left[\begin{array}{cccccccccc}\hfill -1.17& \hfill 0.53& \hfill -1.02& \hfill 1.12& \hfill 2.08& \hfill -1.61& \hfill 1.17& \hfill 2.00& \hfill 3.00& \hfill 3.00\\ \hfill 1.05& \hfill -0.03& \hfill 0.38& \hfill -0.22& \hfill -1.36& \hfill 0.90& \hfill -1.21& \hfill -1.03& \hfill -2.00& \hfill 3.58\\ \hfill -0.30& \hfill -1.00& \hfill 1.11& \hfill -1.69& \hfill -0.76& \hfill 0.99& \hfill 0.71& \hfill -1.44& \hfill -1.00& \hfill 3.00\end{array}\right]$
	k = 1	$\left[\begin{array}{cccccccccc}\hfill -1.34& \hfill 0.32& \hfill -0.83& \hfill 0.78& \hfill 2.06& \hfill -1.50& \hfill 1.45& \hfill 1.81& \hfill 3.00& \hfill 4.01\\ \hfill 0.89& \hfill -0.22& \hfill 0.55& \hfill -0.52& \hfill -1.37& \hfill 1.00& \hfill -0.96& \hfill -1.20& \hfill -2.00& \hfill -2.67\\ \hfill 0.45& \hfill -0.11& \hfill 0.28& \hfill -0.26& \hfill -0.69& \hfill 0.50& \hfill -0.48& \hfill -0.60& \hfill -1.00& \hfill -1.34\end{array}\right]$
Formula 4	k = 3	(−2.00, 3.00, 1.00)
Scores	k = 2	(−2.26, −1.16)
New Point	k = 1	−2.39
Formula 5	k = 3	(−2.00, 3.00, 1.00)
Projections	k = 2	(−2.00, 1.20, 1.00)
New Point	k = 1	(−1.92, 1.28, 0.64)