Results 131 to 140 of about 635,756 (168)

An Existence Test for Root Clusters and Multiple Roots

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1988
Let f be analytic in the interior of the disk \(K(\tilde z;r)\) with center \(\tilde z\) and radius r, and let ...
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Newton's method for multiple roots

Computers & Graphics, 1994
Abstract We investigate the basins of attraction in the complex plane of Newton's method for finding multiple roots and illustrate what happens as two simple roots coalesce to form a double root.
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Square rooting is as difficult as multiplication

Computing, 1979
It is shown that multiplication of numbers and square rooting have the same complexity, i. e. from a program for multiplication one can construct a program for square rooting with the same asymptotic time complexity (1 step≦1 bit-operation) and vice versa.
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POLYNOMIALS WITH MULTIPLE ROOTS AT 1

International Journal of Number Theory, 2014
We prove that every polynomial P(x) = 1 + a1x + ⋯ + adxd∈ ℂ[x] has a root at x = 1 of order at most [Formula: see text], where ε > 0, provided that the quantities H*(P) = max1 ≤ j ≤ d|aj| and d/ log H*(P) are sufficiently large (the order of the root of P at x = 1 is zero if P(1) ≠ 0).
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On the development of iterative methods for multiple roots

Applied Mathematics and Computation, 2013
There are very few optimal fourth order methods for solving nonlinear algebraic equations having roots of multiplicity m. Here we compare 4 such methods, two of which require the evaluation of the (m-1)^s^t root. We will show that such computation does not affect the overall cost of the method.
Neta, Beny, Chun, Changbum, Scott, Melvin   +2 more
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Multiple neurofibromas of the spinal nerve roots

Journal of Clinical Neuroscience, 1995
This report describes a rare case of a suspected neurofibromatosis type 1 patient who had multiple bilateral spinal neurofibromas from the cervical to the sacral spinal dorsal nerve roots. The lesions were readily detected by MR imaging and the largest tumour was successfully resected.
S, Nakagawa, M, Abe, K, Tabuchi
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Multiple idiopathic external root resorption

Oral Surgery, Oral Medicine, Oral Pathology, 1989
An unusual case of multiple idiopathic root resorption involving all of the maxillary and mandibular incisor, canine, and premolar teeth is presented. A review of the literature reveals that this case is unusual in that, although other cases of multiple idiopathic root resorption have been described, the site of the resorption has been at the cervical ...
K R, Postlethwaite, M, Hamilton
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A Search for Root-Multiples

The Mathematics Teacher, 1976
Learn what “root-multiples” are and then use them to generate interesting progressions.
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Asymptotic distributions of the latent roots with multiple population roots in multiple discriminant analysis

Annals of the Institute of Statistical Mathematics, 1978
Asymptotic expansions are derived for the confluent hypergeometric function1 F 1(a; c; R, S) with two argument matrices, which appears in the joint density function of the latent roots in multiple discriminant analysis, whenR is “large” and each of the latent roots ofR assumes the general multiplicity.
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RESOLUTION OF MULTIPLE ROOTS OF NONLINEAR POLYNOMIAL SYSTEMS

International Journal of Shape Modeling, 2005
Summary: In this paper we discuss the roots and multiplicities of univariate and bivariate nonlinear polynomial systems and present methods to compute them robustly. For univariate polynomial systems, we propose an algorithm called the Topological Degree Bisection (TDB) algorithm which is developed based on the concept of the topological degree of a ...
Kwang Hee Ko, Takis Sakkalis, Nicholas M. Patrikalakis   +2 more
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