Lower bound for the number of nodes of cubature formulae on the unit ball
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چکیده
منابع مشابه
Orthogonal Polynomials and Cubature Formulae on Spheres and on Balls∗
Orthogonal polynomials on the unit sphere in Rd+1 and on the unit ball in Rd are shown to be closely related to each other for symmetric weight functions. Furthermore, it is shown that a large class of cubature formulae on the unit sphere can be derived from those on the unit ball and vice versa. The results provide a new approach to study orthogonal polynomials and cubature formulae on spheres.
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Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T d. These formulae are used to derive cubature formulae on the surface of the sphere Sd and on the unit ball Bd using connections between cubature for...
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Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T . These formulae are used to derive cubature formulae on the surface of the sphere S and on the unit ball B using connections between cubature formul...
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Orthogonal polynomials on the standard simplex Σ in R are shown to be related to the spherical orthogonal polynomials on the unit sphere S in R that are invariant under the group Z2×· · ·×Z2. For a large class of measures on S cubature formulae invariant under Z2 × · · · × Z2 are shown to be characterized by cubature formulae on Σ. Moreover, it is also shown that there is a correspondence betwe...
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In simulating interstellar dust clouds astrophysicists need high accuracy integration formulae for functions on the sphere. To construct better formu-lae than previously used, almost equidistantly spaced nodes on the sphere and weights belonging to these nodes are required. This problem is closely related to a facility dispersion problem on the sphere and to the theories of spherical designs an...
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ورودعنوان ژورنال:
- J. Complexity
دوره 19 شماره
صفحات -
تاریخ انتشار 2003