Existence Verification for Higher Degree Singular Zeros of Nonlinear Systems (original) (raw)
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Computational fixed point theorems can be used to automatically verify existence and uniqueness of a solution to a nonlinear system of n equations in n variables ranging within a given region of n-space. Such computations succeed, however, only when the Jacobi matrix is nonsingular everywhere in this region. However, in problems such as bifurcation problems or surface intersection problems, the Jacobi matrix can be singular, or nearly so, at the solution. For n real variables, when the Jacobi matrix is singular, tiny perturbations of ...
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