Regularity results for real analytic homotopies |
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| Authors: | Tien-Yien Li John Mallet-Paret James A Yorke |
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| Institution: | (1) Department of Mathematics, Michigan State University, 48824 East Lansing, MI, USA;(2) Institute for Physical Science and Technology, and Department of Mathematics, University of Maryland, 20742 College Park, MD, USA |
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| Abstract: | Summary In this paper, we study two main features of the homotopy curves which we follow when we use the homotopy method for solving the zeros of analytic maps. First, we prove that near the solution the curve behaves nicely. Secondly, we prove that the set of starting points which give smooth homotopy curves is open and dense. The second property is of particular importance in computer implementation.This research was supported by the National Science Foundation under Grants MCS 78-02420 (Li) and MCS-7818858 (Mallet-Paret) and MCS-7818221 (Yorke), by the Army Research office under Grant DAAG-29-80-C-0040 (Li and Yorke) |
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| Keywords: | AMS (MOS) Primary 90B99 Secondary G5H10 |
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