Verifying Topological Indices for Higher-Order Rank Deficiencies

It has been known how to use computational fixed point theorems to verify existence and uniqueness of a true solution to a nonlinear system of equations within a small region about an approximate solution. This can be done in O n3 operations, where n is the number of equations and unknowns. However, these standard techniques are only valid if the Jacobi matrix for the system is nonsingular at the solution. In previous work and a dissertation (of Dian), we have shown, both theoretically and practically, that existence and multiplicity can be verified in a complex setting, and in the real setting for odd multiplicity, when the rank defect of the Jacobi

• Type: Journal
• Year: 2002
• Where: JC
• Authors: R. Baker Kearfott, Jianwei Dian
• Keywords: Computational Fixed Point, JC 2002, Solution, True Solution