An improved Siljak's algorithm for solving polynomial equations converges quadratically to multiple zeros

被引:6
作者
Stolan, JA [1 ]
机构
[1] UNITED TECHNOL CORP,DIV CHEM SYST,SAN JOSE,CA 95148
关键词
polynomials; zeros; roots; algorithms; multiple zeros;
D O I
10.1016/0377-0427(94)00114-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Siljak's method provides a globally convergent algorithm for inclusion of polynomial zeros. The solution procedure is formulated as a minimization process of a positive definite function involving the real and imaginary parts of the polynomial. The main objective of this paper is to propose an improved version of Siljak's algorithm, which exploits the minimizing function to ensure a quadratic convergence to multiple zeros and, at the same time, determine their multiplicity. Time comparisons with other standard zero inclusion methods are provided to demonstrate the efficiency of the proposed improvement of the original algorithm.
引用
收藏
页码:247 / 268
页数:22
相关论文
共 15 条
[1]  
ETKOVIC M, 1989, LECTURE NOTES MATH, V87
[2]  
HANSEN E, 1977, NUMER MATH, V27, P257, DOI 10.1007/BF01396176
[3]  
Hirsch MW., 1974, DIFFERENTIAL EQUATIO
[4]  
JENKINS M, 1974, P MATH SOFTWARE, V2, P84
[5]  
JENKINS M, 1970, NUMER MATH, V20, P252
[6]   A BIBLIOGRAPHY ON ROOTS OF POLYNOMIALS [J].
MCNAMEE, JM .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1993, 47 (03) :391-394
[7]  
MOORE J, 1967, J APPL MATH, V14, P324
[8]   THE LAGUERRE METHOD FOR FINDING THE ZEROS OF POLYNOMIALS [J].
ORCHARD, HJ .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1989, 36 (11) :1377-1381
[9]  
PRESS W, 1986, NUMERICAL RECIPES AR, P259
[10]  
RALSTON A, 1978, 1 COURSE NUMERICAL A