论文标题
牛顿型方法的吸引力和临界曲线的盆地均衡问题
Basins of attraction and critical curves for Newton-type methods in a phase equilibrium problem
论文作者
论文摘要
许多工程问题由非线性方程式的系统描述，这些系统可能在根深蒂固的算法中表现出多种解决方案。几种溶液的存在可能会引起算法中解决方案的复杂吸引力盆地，并对它们的收敛行为产生严重影响。在这项工作中，我们探讨了景点盆地与临界曲线的关系（方程式系统的jacobian的奇异点的轨迹）在平面中使用两个溶液的相位平衡问题，即计算二进制混合物中双偏二酶的关系。结果表明，吸引力和临界曲线盆地的联合使用可以是为特定问题选择最合适的算法的有用工具。
Many engineering problems are described by systems of nonlinear equations, which may exhibit multiple solutions, in a challenging situation for root-finding algorithms. The existence of several solutions may give rise to complex basins of attraction for the solutions in the algorithms, with severe influence in their convergence behavior. In this work, we explore the relationship of the basins of attractions with the critical curves (the locus of the singular points of the Jacobian of the system of equations) in a phase equilibrium problem in the plane with two solutions, namely the calculation of a double azeotrope in a binary mixture. The results indicate that the conjoint use of the basins of attraction and critical curves can be a useful tool to select the most suitable algorithm for a specific problem.
