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Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Multivariable Tangent and Secant qderivative Polynomials
, 2012
"... Abstract. The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable q– environment. The nth qderivatives of the classical qtangent and qsecant are each given two polynomial expressions. The first polynomia ..."
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Cited by 1 (0 self)
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Abstract. The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable q– environment. The nth qderivatives of the classical qtangent and qsecant are each given two polynomial expressions. The first
Computing Bernoulli and Tangent NumbersSummary continued
, 2011
"... Bernoulli numbers are rational numbers Bn defined by the generating function n≥0 ..."
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Bernoulli numbers are rational numbers Bn defined by the generating function n≥0
ON THE IDEALS OF SECANT VARIETIES OF SEGRE VARIETIES
, 2003
"... We establish basic techniques for studying the ideals of secant varieties of Segre varieties. We solve a conjecture of Garcia, Stillman and Sturmfels on the generators of the ideal of the first secant variety in the case of three factors and solve the conjecture settheoretically for an arbitrary n ..."
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Cited by 66 (13 self)
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number of factors. We determine the low degree components of the ideals of secant varieties of small dimension in a few cases.
A TangentSecant Method for Polynomial Complex Root Calculation
 In Proc. ACM Intern. Symp. on Symbolic and Algebraic Computation
, 1993
"... Let a rectangle be given which contains exactly one complex root of a given univariate polynomial. Let the edges of the rectangle be parallel to the coordinate axes. We present a hybrid symbolicnumeric method for constructing a small subrectangle which contains the root. The subrectangle is chosen ..."
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Cited by 2 (0 self)
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such that it contains the intersection of two triangles. The triangles are constructed so as to contain segments of certain algebraic curves that pass through the given rectangle; the intersection of these segments is precisely the complex root. 1 Introduction Any univariate polynomial A 2 C[z] can be represented
EQUATIONS DEFINING SECANT VARIETIES: GEOMETRY AND COMPUTATION
"... Abstract. In the 1980’s, work of Green and Lazarsfeld [10, 11] helped to uncover the beautiful interplay between the geometry of the embedding of a curve and the syzygies of its defining equations. Similar results hold for the first secant variety of a curve, and there is a natural conjectural pictu ..."
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Cited by 2 (0 self)
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picture extending to higher secant varieties as well. We present an introduction to the algebra and geometry used in [20] to study syzygies of secant varieties of curves with an emphasis on examples of explicit computations and elementary cases that illustrate the geometric principles at work. 1.
SECANT DIMENSIONS OF MINIMAL ORBITS: COMPUTATIONS AND CONJECTURES
"... We present an algorithm for computing the dimensions of higher secant varieties of minimal orbits. Experiments with this algorithm lead to many conjectures on secant dimensions, especially of Grassmannians and Segre products. For these two classes of minimal orbits we give a short proof of the relat ..."
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We present an algorithm for computing the dimensions of higher secant varieties of minimal orbits. Experiments with this algorithm lead to many conjectures on secant dimensions, especially of Grassmannians and Segre products. For these two classes of minimal orbits we give a short proof
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