Abstract Various applications in science and engineering depend upon computing real solutions to systems of analytic equations which depend upon real parameters. Locally in the parameter space, the qualitative behavior of the solutions remains the same except at critical parameter values. This article develops a singular value homotopy that aims to compute critical parameter values. Several examples are presented including computing critical parameter values for nonlinear boundary value problems, turning points for a steady-state system connected to learning and memory, and computing the maximum Gaussian curvature of a surface.

中文翻译：

---

用于寻找关键参数值的奇异值同伦

摘要 科学和工程中的各种应用依赖于计算依赖于实参数的解析方程组的实解。在参数空间局部，除临界参数值外，解的定性行为保持不变。本文开发了一个奇异值同伦，旨在计算关键参数值。提供了几个示例，包括计算非线性边界值问题的关键参数值、连接到学习和记忆的稳态系统的转折点，以及计算表面的最大高斯曲率。