Abstract
Applying the method of steepest descent to F(x 1,..., x n ) one obtains a sequence of points ξ v . To obtain conditions for convergence of ξ v , the derived set H of the ξ v in the case of divergence is studied. In this case H is a continuum on which not only grad F vanishes everywhere, but also the rank of the Hessian of F is everywhere less than n-1.
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References
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Communicated by L. Collatz
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Ostrowski, A.M. Contributions to the theory of the method of steepest descent. Arch. Rational Mech. Anal. 26, 257–280 (1967). https://doi.org/10.1007/BF00281659
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DOI: https://doi.org/10.1007/BF00281659