# Continuous Newton's method for polynomials

## Related Articles

- ON THE EFFICIENCY OF NEWTON'S METHOD IN APPROXIMATING ALL ZEROS OF A SYSTEM OF COMPLEX POLYNOMIALS. Renegar, J. // Mathematics of Operations Research;Feb87, Vol. 12 Issue 1, p121
This paper studies the efficiency of an algorithm based on Newton's method is approximating all zeros of a system of polynomials f = (f[sub 1], f[sub 2],..., f[sub n]): C[sup n] ? C[sup n]. The criteria for a successful approximation y of a zero w of f include the following: given e > 0, y is...

- APPLICATION OF NEWTON'S AND CHEBYSHEV'S METHODS TO PARALLEL FACTORIZATION OF POLYNOMIALS. Shi-ming Zheng // Journal of Computational Mathematics;Jul2001, Vol. 19 Issue 4, p347
Discusses the application of Newton's method and Chebyshev's method to parallel factorization of polynomials. Introduction of linear interpolation operators and their properties; Condition for nonsingulity of nonlinear equation; Properties of the parallel iterations for factorization of...

- Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method. GEORGOULIS, EMMANUIL H.; S�LI, ENDRE // IMA Journal of Numerical Analysis;Jan2005, Vol. 25 Issue 1, p205
We consider the hp-version interior penalty discontinuous Galerkin finite-element method (hp-DGFEM) for second-order linear reaction--diffusion equations. To the best of our knowledge, the sharpest known error bounds for the hp-DGFEM are due to Riviï¿½re et al. (1999, Comput. Geosci., 3,...

- On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I. Fagella, N�ria; Jarque, Xavier; Taix�s, Jordi // Proceedings of the London Mathematical Society;Nov2008, Vol. 97 Issue 3, p599
It is known that the Julia set of the Newton method of a non-constant polynomial is connected (Mitsuhiro Shishikura, Preprint, 1990, M/90/37, Inst. Hautes ï¿½tudes Sci.). This is, in fact, a consequence of a much more general result that establishes the relationship between simple...

- On Newtons method for entire functions. Johannes Rückert; Dierk Schleicher // Journal of the London Mathematical Society;Dec2007, Vol. 76 Issue 3, p812
The printed versions of Figures 2 and 4 in the above-mentioned paper were unclear. These figures are reprinted below. Figure 2â€ƒNewton map for a polynomial of degree 9. The channels are clearly visible. Figure 4â€ƒA schematic illustration of some notation in the proof of Theorem 5.1.

- Comparison of Lagrange's and Newton's interpolating polynomials. Srivastava, R. B.; Srivastava, Purushottam Kumar // Journal of Experimental Sciences;Jan2012, Vol. 3 Issue 1, p1
A set of fourteen functions have been considered in various intervals. Lagrange's and Newton's interpolating polynomials have been obtained for each function using a computer program developed in C++ programming language. Average of the maximum percentage error for the functions in Newton's...

- Polynomiography. CHOATE, JON // Consortium;Fall2013, Vol. 105, p8
The article discusses the solutions for solving polynomial equations in secondary mathematics curriculum. It states that several approximation routines such as the Newton's Method and bisection method, quadratic formula, and cubic and quartic formulas were used before the arrival of computers...

- A new efficient algorithm for polynomial interpolation. Smoktunowicz, A.; Wróbel, I.; Kosowski, P. // Computing;Feb2007, Vol. 79 Issue 1, p33
A new backward stable algorithm (Algorithm 2) for polynomial interpolation based on the Lagrange and the Newton interpolation forms is proposed. It is shown that the Aitken algorithm and the scheme of the divided differences can be significantly less accurate than the proposed unconditionally...

- Chebyshev polynomial solutions of a class of second-order nonlinear ordinary differential equations. Yüuksel, Gamze; Güulsu, Mustafa; Sezer, Mehmet // Journal of Advanced Research in Scientific Computing;2011, Vol. 3 Issue 4, p11
In this paper, a matrix method based on Chebyshev collocation points on interval [-1, 1] is proposed for the approximate solution of some second order nonlinear ordinary differential equations with the mixed conditions in terms of Chebyshev polynomials. The method, by means of Chebyshev...