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THE EXISTENCE AND CONSTRUCTION OF RATIONAL GAUSSTYPE QUADRATURE RULES∗
"... Abstract. Consider a hermitian positivedefinite linear functional F, and assume we have m distinct nodes fixed in advance anywhere on the real line. In this paper we then study the existence and construction of nth rational GaussRadau (m = 1) and GaussLobatto (m = 2) quadrature formulas that appr ..."
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Cited by 1 (0 self)
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Abstract. Consider a hermitian positivedefinite linear functional F, and assume we have m distinct nodes fixed in advance anywhere on the real line. In this paper we then study the existence and construction of nth rational GaussRadau (m = 1) and GaussLobatto (m = 2) quadrature formulas
Gausstype quadrature rules for rational functions
 in Numerical Integration IV
"... Abstract. When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as ..."
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Cited by 13 (4 self)
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Abstract. When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so
Algorithm xxx — ORTHPOL: A package of routines for generating orthogonal polynomials and Gausstype quadrature rules

, 1993
"... A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the threeterm recurrence relation satisfie ..."
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Cited by 2 (2 self)
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satisfied by the orthogonal polynomials. Once these are known, additional data can be generated, such as zeros of orthogonal polynomials and Gausstype quadrature rules, for which routines are also provided.
Quadrature rulebased bounds for functions of adjacency matrices
, 2010
"... Bounds for entries of matrix functions based on Gausstype quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, centrality, communicability) that describe pro ..."
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Bounds for entries of matrix functions based on Gausstype quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, centrality, communicability) that describe
ISSN 10689613. ORTHOGONAL POLYNOMIALS AND QUADRATURE ∗
"... Abstract. Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gausstype quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a signvariable m ..."
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Abstract. Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gausstype quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign
SzegőLobatto quadrature rules
"... Gausstype quadrature rules with one or two prescribed nodes are well known and are commonly referred to as GaussRadau and GaussLobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szegő quadrature rules are analogs of Gauss quadrature rules for the int ..."
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Gausstype quadrature rules with one or two prescribed nodes are well known and are commonly referred to as GaussRadau and GaussLobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szegő quadrature rules are analogs of Gauss quadrature rules
Orthogonal Polynomials and Quadrature
 Elec. Trans. Numer. Anal
"... Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gausstype quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a signvariable measure, wh ..."
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Cited by 4 (2 self)
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Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gausstype quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a signvariable measure
unknown title
, 2010
"... We consider rational Gausstype quadrature rules on the interval [−1, 1] with one fixed node in xα = cos(θα) ∈ (−1, 1). The remaining nodes are then chosen inside the interval [−1, 1] to achieve the maximal possible domain of validity in the space of rational functions, while maintaining positive ..."
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We consider rational Gausstype quadrature rules on the interval [−1, 1] with one fixed node in xα = cos(θα) ∈ (−1, 1). The remaining nodes are then chosen inside the interval [−1, 1] to achieve the maximal possible domain of validity in the space of rational functions, while maintaining positive
Complex Gaussian quadrature of oscillatory integrals
, 2008
"... We construct and analyze Gausstype quadrature rules with complexvalued nodes and weights to approximate oscillatory integrals with stationary points of high order. The method is based on substituting the original interval of integration by a set of contours in the complex plane, corresponding to t ..."
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Cited by 19 (8 self)
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We construct and analyze Gausstype quadrature rules with complexvalued nodes and weights to approximate oscillatory integrals with stationary points of high order. The method is based on substituting the original interval of integration by a set of contours in the complex plane, corresponding
Some Unusual Matrix Eigenvalue Problems
 PROCEEDINGS OF VECPAR'98  THIRD INTERNATIONAL CONFERENCE FOR VECTOR AND PARALLEL PROCESSING
, 1999
"... We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the wellknown Gausstype quadrature rules and Lanczos process are reviewed for computing these quadrati ..."
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Cited by 5 (0 self)
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We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the wellknown Gausstype quadrature rules and Lanczos process are reviewed for computing
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