# Jacobian

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(dʒəˈkəʊbɪən) or

## Jacobian determinant

n
(Mathematics) maths a function from n equations in n variables whose value at any point is the n x n determinant of the partial derivatives of those equations evaluated at that point
[named after Karl Gustav Jacob Jacobi]
Translations
jacobien
References in periodicals archive ?
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 determinant?
(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].
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