منابع مشابه
Representation of sparse Legendre expansions
We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M N nonzero terms from only 2M function resp. derivative values f (1), j = 0, . . . , 2M − 1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evalu...
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One may think of Vassiliev invariants (see BN1], B], BL], Ko] and V1,2]) as link invariants with certain nilpotency. From this point of view, it is not surprising that Milnor's link invariants ((M1,2]) are of the same nature as Vassiliev invariants ((BN2], L2]). We give a conceptually clearer proof of this fact here by synthesizing Kontse-vich's construction of Vassiliev invariants and Milnor i...
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We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra. As applications, we compute Shimura curve parametrizations of elliptic curves over a totally real field, including the image of CM points, and equations for Shimura curves.
متن کاملReconstruction of sparse Legendre and Gegenbauer expansions
Recently the reconstruction of sparse trigonometric polynomials has attained much attention. There exist recovery methods based on random sampling related to compressed sensing (see e.g. [17, 10, 5, 4] and the references therein) and methods based on deterministic sampling related to Prony–like methods (see e.g. [15] and the references therein). Both methods are already generalized to other pol...
متن کاملAsymptotic expansions of Legendre series coefficients for functions with endpoint singularities
Avram Sidi Computer Science Department, Technion – Israel Institute of Technology, Haifa 32000, Israel E-mail: [email protected]; URL: http://www.cs.technion.ac.il/~asidi/ Abstract. Let ∑∞ n=0 en[f ]Pn(x) be the Legendre expansion of a function f (x) on (−1, 1). In this work, we derive an asymptotic expansion as n → ∞ for en[f ], assuming that f ∈ C∞(−1, 1), but may have arbitrary algebra...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1999
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181070407