A class of exponential quadratically convergent iterative formulae for unconstrained optimization

Kahya E

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A class of exponential quadratically convergent iterative formulae for unconstrained optimization

机译：用于无约束优化的一类指数二次收敛迭代公式

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For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which converges quadratically. This paper presents a class of exponential iterative formulae. Convergence analyses show that the proposed methods converge quadratically. The efficiencies of the methods are analyzed in terms of the most popular and widely used criterion in comparison with the classical Newton method using five test functions. Numerical results indicate that one of the new exponential iterative formulae is effective and comparable to well-known Newton's method. (c) 2006 Elsevier Inc. All rights reserved.

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《Applied mathematics and computation》 |2007年第2期|共8页
作者
Kahya E;
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正文语种 eng
中图分类应用数学;
关键词
unconstrained optimization; Newton method; exponential iterative formulae; order of convergence; quadratic convergence; test functions; NEWTONS METHOD; 3RD-ORDER CONVERGENCE; VARIANT;

机译：无约束优化;牛顿法;指数迭代公式;收敛阶次;二次收敛;测试函数;牛顿法;3RD阶收敛;变数;

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1. A class of exponential quadratically convergent iterative formulae for unconstrained optimization [J] . Kahya E Applied mathematics and computation . 2007,第2期

机译：用于无约束优化的一类指数二次收敛迭代公式
2. On a class of quadratically convergent iteration formulae [J] . Mamta, Kanwar V, Kukreja VK, Applied mathematics and computation . 2005,第3期

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3. A one-parameter family of quadratically convergent iteration formulae [J] . Changbum Chun Applied mathematics and computation . 2007,第1期

机译：一参数系列二次收敛迭代公式
4. On the Convergence of the Iterative Linear Exponential Quadratic Gaussian Algorithm to Stationary Points [C] . Vincent Roulet, Maryam Fazel, Siddhartha Srinivasa, Annual American Control Conference . 2020

机译：迭代线性指数二次高斯算法对平稳点的收敛性
5. The eigenstep method: A new iterative method for unconstrained quadratic optimization. [D] . Battaglia, John P. 2005

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6. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization [O] . Xiangrong Li, Xupei Zhao, Xiabin Duan, -1

机译：具有函数值信息和N步二次收敛的共轭梯度算法无约束优化
7. A Globally and Quadratically Convergent Algorithm with Efficient Implementation for Unconstrained Optimization∗ [O] . Yaguang Yang 2014

机译：无约束优化的高效实现的全局和二次收敛算法*
8. Quadratically Convergent O(square root of nL-Iteration) Algorithm for Linear Programming. [R] . Ye, Y., Gueler, O., Tapia, R. A., 1991

机译：线性规划的二次收敛O（nL迭代的平方根）算法。

A class of exponential quadratically convergent iterative formulae for unconstrained optimization

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