论文标题
基于合理插值的自加工根搜索和优化方法
Self-accelerating root search and optimisation methods based on rational interpolation
论文作者
论文摘要
基于Barycentric有理插值的迭代方法得出了表现出加速收敛顺序的迭代方法。对于单变量的根搜索，无衍生方法方法接近二次收敛和第一衍生方法方法方法分数收敛。为了单变量优化，无衍生方法的收敛顺序接近1.62，而第一衍生方法的顺序接近2.42。通常，在低内存迭代方法方面发现了性能优势。在优化问题中，在每个步骤中计算目标函数和梯度时，全书迭代方法渐近地收敛于1.8倍的速度比SECANT方法快1.8倍。还提出了用于多元根搜索和优化的框架，尽管没有发现实际参数选择。
Iteration methods based on barycentric rational interpolation are derived that exhibit accelerating orders of convergence. For univariate root search, the derivative-free methods approach quadratic convergence and the first-derivative methods approach cubic convergence. For univariate optimisation, the convergence order of the derivative-free methods approaches 1.62 and the order of the first-derivative methods approaches 2.42. Generally, performance advantages are found with respect to low-memory iteration methods. In optimisation problems where the objective function and gradient is calculated at each step, the full-memory iteration methods converge asymptotically 1.8 times faster than the secant method. Frameworks for multivariate root search and optimisation are also proposed, though without discovery of practical parameter choices.
