Results 1  10
of
894,470
Calculation of Gauss–Kronrod Quadrature Rules
 Mathematics of Computation
, 1997
"... Abstract. The Jacobi matrix of the (2n+1)point GaussKronrod quadrature rule for a given measure is calculated efficiently by a fiveterm recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the JacobiKronrod matrix analytically. The nodes and ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
Abstract. The Jacobi matrix of the (2n+1)point GaussKronrod quadrature rule for a given measure is calculated efficiently by a fiveterm recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the JacobiKronrod matrix analytically. The nodes
COMPUTATION OF GAUSSKRONROD QUADRATURE RULES
"... Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)point GaussKronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial spectral ..."
Abstract
 Add to MetaCart
Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)point GaussKronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial
COMPUTATION OF GAUSSKRONROD QUADRATURE RULES
"... Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)point GaussKronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial spectral ..."
Abstract
 Add to MetaCart
Abstract. Recently Laurie presented a new algorithm for the computation of (2n+1)point GaussKronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n + 1 from certain mixed moments, and then computes a partial
Stieltjes polynomials and the error of GaussKronrod quadrature formulas
, 1998
"... . The GaussKronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the GaussKronrod scheme. An ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
. The GaussKronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the GaussKronrod scheme
Computation of GaussKronrod Quadrature Rules with NonPositive Weights
 Math. Comp
, 1999
"... Recently Laurie presented a fast algorithm for the computation of (2n + 1)point GaussKronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of GaussKronrod quadrature rules with complex conjugate nodes and weights or w ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
Recently Laurie presented a fast algorithm for the computation of (2n + 1)point GaussKronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of GaussKronrod quadrature rules with complex conjugate nodes and weights
Ultraspherical GaussKronrod Quadrature is not possible for lambda > 3
"... . With the help of a new representation of the Stieltjes polynomial it is shown by using Bessel functions that the Stieltjes polynomial with respect to the ultraspherical weight function with parameter has only few real zeros for > 3 and suciently large n . Since the nodes of the GaussKronrod ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
. GaussKronrod quadrature, Stieltjes polynomials, orthogonal polynomials, Bessel functions AMS subject classication. 33C10, 33C45, 42C05, 65D32 1. Introduction and Main Results Let be a nonnegative nontrivial measure and let p n (x; d) := p n (x) = x n + : : : , n 2 N , be the monic polynomials
On Product Integration With GaussKronrod Nodes
, 1998
"... GaussKronrod product quadrature formulas for the numerical approximation of R 1 \Gamma1 k(x)f(x) dx are shown to converge for every Riemann integrable f , and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application to the ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
GaussKronrod product quadrature formulas for the numerical approximation of R 1 \Gamma1 k(x)f(x) dx are shown to converge for every Riemann integrable f , and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application
Positivity of GaussKronrod formulae for a certain ultraspherical weight function
"... . In this note, we show that for a suciently large number of nodes, the weights of the GaussKronrod quadrature formulae with respect to the weight function w(x) = 1 x 2 5=2 are positive. Since this weight function is a limit case in a certain sense, we are led to some conjectures concerning the ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. In this note, we show that for a suciently large number of nodes, the weights of the GaussKronrod quadrature formulae with respect to the weight function w(x) = 1 x 2 5=2 are positive. Since this weight function is a limit case in a certain sense, we are led to some conjectures concerning
Generalized Stieltjes Polynomials and Rational GaussKronrod Quadrature
"... Generalized Stieltjes polynomials are introduced and their asymptotic properties outside the support of the measure studied. As applications, we prove the convergence of sequences of interpolating rational functions, whose poles are partially fixed, to Markov functions and give an asymptotic estimat ..."
Abstract
 Add to MetaCart
estimate of the error of rational GaussKronrod quadrature formulae when functions which are analytic on some neighbourhood of the set of integration are considered.
High confidence visual recognition of persons by a test of statistical independence
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 1993
"... Abstruct A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person’s face is the detailed texture of each eye’s iris: An estimate of its statistical complexity in a samp ..."
Abstract

Cited by 596 (8 self)
 Add to MetaCart
different eyes is passed almost certainly, whereas the same test is failed almost certainly when the compared codes originate from the same eye. The visible texture of a person’s iris in a realtime video image is encoded into a compact sequence of multiscale quadrature 2D Gabor wavelet coefficients
Results 1  10
of
894,470