Abstract
Two scalar labelings are introduced for obtaining approximate solutions to systems of nonlinear equations by simplicial approximation. Under reasonable assumptions the new scalar-labeling algorithms are shown to follow, in a limiting sense, homotopy paths which can also be tracked by piecewise linear vector labeling algorithms. Though the new algorithms eliminate the need to pivot on a system of linear equations, the question of relative computational efficiency is unresolved.
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The work of this author was supported in part by NSF Grant No. MCS-77-15509 and by ARO Grant No. DAAG-29-78-G-0160.
The work of this author was supported in part by ONR Grant No. N00014-75-C-0495 and NSF Grant No. 81058.
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Garcia, C.B., Gould, F.J. Scalar labelings for homotopy paths. Mathematical Programming 17, 184–197 (1979). https://doi.org/10.1007/BF01588243
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DOI: https://doi.org/10.1007/BF01588243