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Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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polynomials feZ[X] into irreducible factors in Z[X]. Here we call f ~ Z[X] primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. [8]. Its running time, measured in bit operations, is O(nl2+n9(log[fD3). Here f~Tl[X] is the polynomial
Least angle regression
, 2004
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1326 (37 self)
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to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm
Asymptotic coefficients of Hermite function series
 J. Comput. Phys
, 1984
"... By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. C ..."
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Cited by 10 (0 self)
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. Comp. Phys. 45 (1982), 4549) for infinite or semiinfinite domains. Like Chebyshev series, the Hermite coefficients are asymptotically given by the sum of two types of terms: (i) stationary point (steepest descent) contributions and (ii) residues at the poles off(z), the function being expanded as a
Pedestrian Detection Using Wavelet Templates
 in Computer Vision and Pattern Recognition
, 1997
"... This paper presents a trainable object detection architecture that is applied to detecting people in static images of cluttered scenes. This problem poses several challenges. People are highly nonrigid objects with a high degree of variability in size, shape, color, and texture. Unlike previous app ..."
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Cited by 277 (23 self)
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This paper presents a trainable object detection architecture that is applied to detecting people in static images of cluttered scenes. This problem poses several challenges. People are highly nonrigid objects with a high degree of variability in size, shape, color, and texture. Unlike previous
Barycentric Hermite interpolation
 SIAM J. Sci. Comput
"... Abstract. Let z1,..., zK be distinct grid points. If fk,0 is the prescribed value of a function at the grid point zk, and fk,r the prescribed value of the rth derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates ..."
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Cited by 2 (0 self)
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Abstract. Let z1,..., zK be distinct grid points. If fk,0 is the prescribed value of a function at the grid point zk, and fk,r the prescribed value of the rth derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates
HERMITE ORTHOGONAL RATIONAL FUNCTIONS
"... Dedicated to William B. Jones on the occasion of his 70th birthday ABSTRACT. We recount previous development of dfold doubling of orthogonal polynomial sequences and give new results on rational function coefficients, recurrence formulas, continued fractions, Rodrigues ’ type formulas, and differen ..."
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, and differential equations, for the general case and, in particular, for the dfold Hermite orthogonal rational functions. 1. Introduction. Orthogonal
Generalized GaussHermite Filtering
, 2006
"... We consider a generalization of the GaussHermite filter (GHF), where the filter density is represented by a Hermite expansion with leading Gaussian term. Thus the usual GHF is included as a special case. The moment equations for the time update are solved stepwise by GaussHermite integration, and ..."
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Cited by 2 (1 self)
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We consider a generalization of the GaussHermite filter (GHF), where the filter density is represented by a Hermite expansion with leading Gaussian term. Thus the usual GHF is included as a special case. The moment equations for the time update are solved stepwise by GaussHermite integration
On the Hermite interpolation polynomial
"... Abstract. The Newton form for the Hermite interpolation polynomial using the divided differences with multiple knots is proved. Using this representation, sufficient conditions for the convergence of the sequence of Hermite interpolation polynomials are established. One extends this way a result obt ..."
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obtained by M. Ivan, regarding to sufficient conditions for the uniform convergence of the sequence of Lagrange polynomials. 2010 Mathematics Subject Classification. 41A05; 65D05. Key words and phrases. Hermite interpolation polynomial, divided difference with multiple knots, uniform convergence. 1.
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