Speed of convergence of Newton-like iterations in an algebraic domain can be affected heavily by the increasing cost of each step, so much so that a quadratically convergent algorithm with complex steps may be comparable to a slower one with simple steps. This note gives two examples: solving algebraic and first-order ordinary differential equations using the MACSYMA algebraic manipulation system, demonstrating this phenomenon. The relevant programs are exhibited in the hope that they might give rise to more widespread application of these techniques.
University of California, Berkeley;
机译:Calogero型投影-代数离散近似方案内Banach空间中线性和非线性微分算子方程的解存在和收敛性分析
机译:一类具有二次非线性的代数微分方程的多项式解
机译:动力系统非线性偏差演化方程的代数动力学解及代数动力学算法
机译:与线性代数方程组有关的向量微分方程的级数解
机译:非线性高指数微分代数方程的有效数值解。
机译:一类一般的二维非线性方程的亚纯解与代数逆散射法联系起来
机译:代数和微分方程的级数解:线性和二次代数收敛的比较