Fractance analog realization using one order Newton method

机译：用一阶牛顿法实现分数阶模拟

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Fractional calculus is a novel powerful tool for non-linear signal processing. This paper realizes the arbitrary order fractance of fractional calculus based on one order Newton process by solving the positive real root of the n-order equation as the approximation of the fractance. The condition under which the one order Newton process can be convergent is discussed. For semi-order fractance realization, the Steffensen method is used to accelerate its iteration process, which shows a good performance. We compare our method with others and present the analog passive realizations scheme of the arbitrary order fractance in the end.

机译：小数演算是一种用于非线性信号处理的新颖强大工具。本文通过求解n阶方程的正实根作为分数的逼近，基于一阶牛顿法实现分数阶微积分的任意阶分数。讨论了一阶牛顿过程可以收敛的条件。对于半阶分数实现，使用Steffensen方法来加速其迭代过程，从而显示出良好的性能。我们将我们的方法与其他方法进行比较，最后提出任意阶数分数的模拟无源实现方案。

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来源
《IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications vol.2; 20050808-12; Beijing(CN)》|2005年|P.1127-1130|共4页
会议地点 Beijing(CN)
作者
LIAO Ke; YUAN Xiao; PU Yi-fei; ZHOU Ji-liu;
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作者单位

School of Electronic and Information Sichuan University China 610064;

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原文格式 PDF
正文语种 eng
中图分类无线通信;
关键词
fractional calculus; fractance; newton method; analog realization;

机译：分数演算；分数；牛顿法；模拟实现;

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1. DESIGN OF -1/2~n ORDER ANALOG FRACTANCE APPROXIMATION CIRCUIT USING CONTINUED FRACTIONS DECOMPOSITION [J] . LIU YAN, PU YI-FEI, ZHOU JI-LIU, Journal of Circuits, Systems, and Computers . 2012,第4期

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2. An Application of Newton Type Iterative Method for Lavrentiev Regularization for Ill-Posed Equations: Finite Dimensional Realization [J] . Santhosh George, Suresan Pareth IAENG International Journal of Applied Mathematics . 2012,第3期

机译：牛顿型迭代法在不适定方程Lavrentiev正则化中的应用：有限维实现
3. Projection-iteration Realization on the Newton-Kantorovich Method for Solving Nonlinear Integral Equations [J] . L.L. Hart, N.V. Polyakov Journal of automation and information sciences . 2012,第1期

机译：牛顿-坎托罗维奇方法求解非线性积分方程的投影迭代实现
4. Fractance analog realization using one order Newton method [C] . Liao Ke, Yuan Xiao, Pu Yi-fei, . 2005

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5. Advancements in finite element methods for Newtonian and non-Newtonian flows. [D] . Galvin, Keith J. 2013

机译：牛顿和非牛顿流的有限元方法的进展。
6. On Newtons Method of Approximation [O] . Henry B. Fine 1916

机译：关于牛顿的近似方法
7. On the realization of the Wolfe conditions in reduced quasi-Newton methods for equality constrained optimization [O] . Jean Charles Gilbert 1997

机译：关于等式约束优化的简化拟牛顿法中沃尔夫条件的实现

Fractance analog realization using one order Newton method

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