Approximation of Fractional Capacitors (1/s)^(1/n) by a Regular Newton Process
作者： G. Carlson , C. Halijak
关键词: Discrete mathematics 、 Algebraic expression 、 Domain (mathematical analysis) 、 Integer 、 Real number 、 Mathematics 、 Order (ring theory) 、 Iterative method 、 Convergence (routing) 、 Numerical analysis
摘要: This paper exhibits a third-order Newton process for approximating (l/s)^{1/n} , the general fractional capacitor, any integer n > 1. The approximation is based on predistortion of algebraic expression f(x) = x^{n} - 0 . resulting in real variables (resistive networks) has unique property preserving upper and lower approximations to th root number Any which possesses this regular. variable theory regular processes presented because motivation lies domain. Realizations 1/3 1/4 order capacitor are presented.
sci-hub.se 参考文章(6)
Einar Hille, Ralph S. Phillips, Functional Analysis And Semi-Groups ,(1948)
J. F. Traub, Comparison of iterative methods for the calculation of nth roots Communications of The ACM. ,vol. 4, pp. 143- 145 ,(1961) , 10.1145/366199.366252
J. F. Traub, On a class of iteration formulas and some historical notes Communications of The ACM. ,vol. 4, pp. 276- 278 ,(1961) , 10.1145/366573.366606
G. Carlson, C. Halijak, Approximations of Fixed Impedances IRE Transactions on Circuit Theory. ,vol. 9, pp. 302- 303 ,(1962) , 10.1109/TCT.1962.1086946
R. Lerner, The Design of a Constant-Angle or Power-Law Magnitude Impedance IEEE Transactions on Circuit Theory. ,vol. 10, pp. 98- 107 ,(1963) , 10.1109/TCT.1963.1082094
Francis Begnaud Hildebrand, Introduction to numerical analysis International Series in Pure and Applied Mathematics. ,(1974)