K. Madsen, A Root-Finding Algorithm Based on Newton's Method, BIT, 13 (1973), pp. 71-75. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Approximating Complex Polynomial Zeros: Modified Weyl's Quadtree.. - Pan (1996) (1 citation) (Correct)
....other major approaches to polynomial rootfinding as well as some history of Weyl s classical approach. 1. 2 The Functional Iteration Approach Practical approximation of the zeros of p(x) presently relies on iterative algorithms based on the Newton, Laguerre, and Jenkins Traub iteration processes [M73], MR75] HPR77] F81] JT70] JT72] IMSL87] The most celebrated example is Newton s iteration, x i 1 = x i Gamma p(x i ) p 0 (x i ) i = 0; 1; which starts with some initial x 0 and is supposed to converge to a zero z j of p(x) If it does, the same process can be recursively ....
K. Madsen, A Root-Finding Algorithm Based on Newton's Method, BIT, 13 (1973), pp. 71-75.
Solving A Polynomial Equation: Some History And Recent Progress - Pan (1997) (27 citations) (Correct)
....of the zeros of polynomials of small and moderately large degrees. At least three such approaches should be cited here: Jenkins and Traub s recursive algorithm, based on shifts of the variable and reversions of the polynomial [JT70] JT72] IMSL87] some variations of Newton s iteration [M73], MR75] and Laguerre s method [HPR77] F81] and [NAG88] rootfinder CO2AGF) all of which first approximate a single zero z of the input polynomial p(x) shift to the next input polynomial p(x) x z) and then recursively repeat these steps to approximate all other zeros of p(x) For most ....
K. MADSEN, A root-finding algorithm based on Newton's method, BIT, 13 (1973), pp. 71--75.
Algebraic Algorithms - Díaz, Emiris, Kaltofen, Pan (Correct)
.... of such algorithms, the practical heuristic champions in efficiency (in terms of computer time and memory space used, according to the results of many experiments) are various modifications of Newton s iteration, z(i 1) z(i) Gamma a(i)p(z(i) p 0 (z(i) a(i) being the step size parameter [Madsen 1973], Laguerre s method [Hansen et al. 1977, Foster 1981] and the randomized Jenkins Traub algorithm [Jenkins and Traub 1970] all three for approximating a single zero z of p(x) which can be extended to approximating other zeros by means of deflation of the input polynomial via its numerical ....
K. Madsen. A root-finding algorithm based on Newton's method. BIT, 13:71--75, 1973.
Algebraic Algorithms - Díaz, Kaltofen, Pan (1997) (Correct)
.... of such algorithms, the practical heuristic champions in efficiency (in terms of computer time and memory space used, according to the results of many experiments) are various modifications of Newton s iteration, z(i 1) z(i) Gamma a(i)p(z(i) p 0 (z(i) a(i) being the step size parameter [Mad73] Laguerre s method [HPR77, Fos81] and the randomized Jenkins Traub algorithm [JT70] all three for approximating a single zero z of p(x) which can be extended to approximating other zeros by means of deflation of the input polynomial via its numerical division by x Gamma z. For simultaneous ....
K. Madsen. A root-finding algorithm based on Newton's method. BIT, 13:71--75, 1973.
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