Graphics Reference
In-Depth Information
the approximated Hessian is positive definite. This falls into a more general class of
techniques called
trust regionmethods
.
More details about these algorithms (e.g. choice of step size, termination crite-
ria, search directions, pitfalls) can be found in numerical optimization textbooks
(e.g., [
118
,
351
]). Implementations of the algorithms in pseudocode can be found in
Press et al. [
374
].
As discussed in Section
6.5.3.2
, the structure of the Jacobian matrix has critical
implications for designing a fast numerical optimization algorithm. In particular, if
J
t
), the
computations should be arranged so that needless multiplications and additions of
elements known to be 0 are avoided.
(
θ
)
is sparse (that is, each element of
f
only depends on a few elements of
θ
