Abstract
The authors in a previous paper presented a method for finding all solutions to a system of n nonlinear equations in n unknowns. The explicit calculation of the solutions was based upon a simplicial pivoting algorithm. In this paper we present a different approach for that calculation which is based upon the continuation method and differential equations. This new approach creates new theoretical insights especially relative to the underlying homotopy and to globality. Also it may be more efficient computationally. First we review the key ideas in obtaining all solutions and, using our new approach, substantially simplify the proofs of, the previous paper. Then we show how to make the continuation method global. Finally we apply this global continuation method to find all solutions. Observe also that the global continuation method herein presented is useful for solving general homotopy equations, and not just for finding all solutions.
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Garcia, C.B., Zangwill, W.I. (1980). Global Continuation Methods for Finding all Solutions to Polynomial Systems of Equations in N Variables. In: Fiacco, A.V., Kortanek, K.O. (eds) Extremal Methods and Systems Analysis. Lecture Notes in Economics and Mathematical Systems, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46414-0_25
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DOI: https://doi.org/10.1007/978-3-642-46414-0_25
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