论文信息 - Higher-order iteration functions for simultaneously approximating polynomial zeros

Higher-order iteration functions for simultaneously approximating polynomial zeros

Two new families of higher-order iteration functions for simultaneously improving approximations to all the zeros of a polynomial are presented. The resulting iteration schemes exhibit improved R-order convergence

George Loizou | G. Loizou

[1] Jürgen Herzberger,et al. On the Convergence Speed of Some Algorithms for the Simultaneous Approximation of Polynomial Roots , 1974 .

[2] Allan Borodin,et al. The computational complexity of algebraic and numeric problems , 1975, Elsevier computer science library.

[3] Emeric Deutsch. Lower bounds for the Perron root of a non-negative irreducible matrix , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.

[4] Henry C. Thacher,et al. Applied and Computational Complex Analysis. , 1988 .

[5] Mary Shaw,et al. On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives , 1974, JACM.

[6] J. Traub. Iterative Methods for the Solution of Equations , 1982 .

[7] E. Seneta. Non-negative matrices;: An introduction to theory and applications , 1973 .

[8] George Loizou,et al. An algorithm for the total, or partial, factorization of a polynomial , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[9] George Loizou,et al. A class of Iteration functions for improving, simultaneously, approximations to the zeros of a polynomial , 1975 .

[10] Götz Alefeld,et al. Über Simultanverfahren zur Bestimmung reeller Polynomwurzeln , 1974 .

[11] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[12] C. Pan,et al. Multiple solutions of nonlinear equations: Roots of polynomials , 1980 .