724 Chapter 16 Numerical Methods
n−1
j=1
AV
j
− α
nj
N
c
j
= λV
A
⎛
⎝
n−1
j=1
c
j
v
j
⎞
⎠
−
⎛
⎝
n−1
j=1
α
nj
c
j
⎞
⎠
N =λV
AV −
N
T
AV
N =λv
(I − NN
T
)AV = λV
Therefore, max Q(V) = λ
n−1
= Q(V
n−1
),whereλ
n−1
is the maximum eigenvalue
corresponding to the eigenvector V
n−1
of (I − NN
T
)A. Note that n − 1 of the eigen-
vectors are in {N}
⊥
. The remaining eigenvector is V
n
= A
Adj
N,whereAA
Adj
=
(det A)I and λ
n
= 0.
16.3 Least-Squares Fitting
Least-squares fitting is the process of selecting a parameterized equation that repre-
sents a discrete set of points in a continuous manner. The parameters are estimated by
minimizing a nonnegative function of the parameters. This section discusses fitting
by lines, planes, quadratic curves, and quadric surfaces.
16.3.1 Linear Fitting of Points ( x
x
x
, f
f
f
( x