Barry H. Dayton

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This paper presents algorithms for computing the multiplicity structure of a zero to a polynomial system. The zero can be exact or approximate with the system being intrinsic or empirical. As an application, the dual space theory and methodology are utilized to analyze deflation methods in solving polynomial systems, to establish tighter deflation bound,(More)
This paper presents an algorithm and its implementation for computing the approximate GCD (greatest common divisor) of multivariate polynomials whose coefficients may be inexact. The method and the companion software appears to be the first practical package with such capabilities. The most significant features of the algorithm are its robustness and(More)
As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an algorithm for computing the multiplicity structure, proposes a depth-deflation method for accurate computation of multiple zeros, and introduces the basic algebraic theory of the(More)
The rules of T cell positioning within virus-infected respiratory tract tissues are poorly understood. We therefore marked cervical lymph node or spleen cells from Sendai virus (SeV) primed mice and transferred lymphocytes to animals infected with SeV expressing an enhanced green fluorescent protein (SeV-eGFP). Confocal imaging showed that when T cells(More)
Generic realizations of configurations of lines as reducible projective varieties in Pn are constructed numerically. Examples are taken from projections of abstract seminormal configurations and the classical geometry related to Schläfli’s double-six configuration. The ideal defining the homogeneous coordinate ring of a realization is calculated along with(More)
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