On Jacobian matrices for flows
نویسندگان
چکیده
منابع مشابه
Nilpotent Symmetric Jacobian Matrices and the Jacobian Conjecture Ii
It is shown that the Jacobian Conjecture holds for all polynomial maps F : k → k of the form F = x + H , such that JH is nilpotent and symmetric, when n ≤ 4. If H is also homogeneous a similar result is proved for all n ≤ 5. Introduction Let F := (F1, . . . , Fn) : C → C be a polynomial map i.e. each Fi is a polynomial in n variables over C. Denote by JF := (i ∂xj )1≤i,j≤n, the Jacobian matrix ...
متن کاملOptimal direct determination of sparse Jacobian matrices
It is well known that a sparse Jacobian matrix can be determined with fewer function evaluations or automatic differentiation passes than the number of independent variables of the underlying function. In this paper we show that by grouping together rows into blocks one can reduce this number further. We propose a graph coloring technique for row partitioned Jacobian matrices to efficiently det...
متن کاملUnipotent Jacobian Matrices and Univalent Maps
The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for C maps is explored here. Some results known in the polynomial case are extended to the C context, and some special cases are resolved.
متن کاملSchur Flows for Orthogonal Hessenberg Matrices
We consider a standard matrix ow on the set of unitary upper Hessenberg matrices with nonnegative subdiagonal elements. The Schur parametrization of this set of matrices leads to ordinary diier-ential equations for the weights and the parameters that are analogous with the Toda ow as identiied with a ow on Jacobi matrices. We derive explicit diierential equations for the ow on the Schur paramet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos: An Interdisciplinary Journal of Nonlinear Science
سال: 2005
ISSN: 1054-1500,1089-7682
DOI: 10.1063/1.1854031