%0 Journal Article
%T Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Mehrpouya, Mohammad Ali
%D 2022
%\ 02/01/2022
%V 3
%N 1
%P 53-58
%! Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian
%K Nonlinear equations
%K Newton' s method
%K Singular Jacobian
%K Continuation method
%R 10.22060/ajmc.2021.20487.1068
%X It is well known that, one of the useful and rapid methods for a nonlinearsystem of algebraic equations is Newton's method. Newton's method has at leastquadratic convergence when the Jacobian is a nonsingular matrix in a neighborhoodof the solution. In this paper, a differential continuation method is presented forsolving the nonlinear system of algebraic equations whose Jacobian matrix is singularat the solution. For this purpose, at first, an auxiliary equation named the homotopyequation is constructed. Then, by differentiating from the homotopy equation, asystem of differential equations is replaced instead of the target problem and solved. Inother words, the solution of the nonlinear system of algebraic equations with singularJacobian is transformed to the solution of a system of differential equations. Somenumerical tests are presented at the end and the computational efficiency of themethod is described.
%U https://ajmc.aut.ac.ir/article_4644_785d5e6be499cc04dc52ada3b7c02cee.pdf