Lemma 1 (Jacobian
of the symmetric square root of a positive definite matrix).
Model analysis was applied on the Jacobian
matrix assuming zero V.
Another challenge comes from the application of the widely used nonlinear method, the Newton-Raphson method, where the Jacobian
matrix needs to be updated and solved at every Newton (nonlinear) iteration, which makes the solution very time consuming for large problems.
There, Zhang chose to grapple with the Jacobian
conjecture, a problem first posed in 1939 that has to date not been proven, for his thesis.
In paper  other factors that influence the performances of parallel solving equations systems with iterative methods were experimentally identified: a distribution of non-zero elements along and around the main diagonal of the associated matrix, the ratio between the number of nonzero elements inside and outside of Jacobian
submatrix for each partition in part and of course the number of partitions.
In sharp contrast to the benchmark configuration, the GDP fraction of government purchases from the consumption sector is found to appear in the model's Jacobian
matrix and thus affects its local stability properties.
Appendices present additional proofs on related topics including potential theory, oscillating pseudopolynomials, the universal function, and local action of the Jacobian
In which science would you encounter a Jacobian
(3) recalculation of a filtered Jacobian
matrix B obtained by means of a correlation filter,
For disease-free equilibrium (DFE), it is easy to calculate that the Jacobian
matrix of system (3) at DFE has eigenvalues [[lambda].sub.1] = -d and [[lambda].sub.2] = -[mu].