This leads to expressing the basic Jacobian matrix
(1) for the total number of fingers.
As in the classical case, the Jacobian matrix
of H(Z, y) with respect to y, denoted by [partial derivative]H/[partial derivative]y is the matrix whose entries are [partial derivative][H.
It is also possible to compute gradients (a special case of Jacobians) of structured computations by exposing the sparsity in an associated extended Jacobian matrix
[Coleman and Jonsson 1999].
A second concept of interaction strength, advanced by May (1973), are the elements in the Jacobian matrix
where [J] is the Jacobian matrix
, [[phi]] is a column vector containing the solution at the iteration indicated by the super index and [F[([phi]).
When the forward model is solved, the sensitivity map, also known as Jacobian matrix
, can then be defined.
And we also can derive the Jacobian matrix
from the velocity equation to judge the singular position.
is the joint variables vector and J the Jacobian matrix
For the applications that we are interested in, n is usually large, and in this case, the algorithm has three expensive operations: the evaluation of F(x), the construction of the Jacobian matrix
, and the solution of the Jacobian system.
where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with J as the Phantom jacobian matrix
n] to (1) is singular if the Jacobian matrix
at z, [D.
Model food chains of varying lengths and complexities, as represented by the well-known Jacobian matrix
of linearized effects at equilibrium densities, were then examined.