Orthogonal Polynomials: Computation and Approximation

By Walter Gautschi. 2004

532 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d27826aea00c37e5e3f372d2b4e61237d8d08594

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In Applied Mathematics

Citations in the corpus

Product Gauss cubature over polygons based on Green’s integration formula (2007, background): “[7] for the role of “modified” moments in connection with univariate orthogonal polynomials, and [6] for the theory of multivariate orthogonal polynomials.”
On Sobolev orthogonal polynomials (2014, unknown): “It should be mentioned that computation of Sobolev orthogonal polynomials is discussed in [40, 42], where several algorithms are provided.”
ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS (2012, unknown): “[13]), or explicitly with the Rodrigues’ formula:”
Meixner-Type Results for Riordan Arrays and Associated Integer Sequences (2010, background): “While partly expository in nature, the note assumes a certain familiarity with integer sequences, generating functions, orthogonal polynomials [4, 10, 31], Riordan arrays [26, 30], production matrices [8, 24], and the integer Hankel transform [1, 6, 17].”
Robust reprojection methods for the resolution of the Gibbs phenomenon (2006, methodology): “Consequently, the generated orthogonal poly approach those which are orthogonal under the continuous inner product [10].”
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type (2012, background): “In[5]:= N@Max@al al160 - 1, be be160 - 1DD”
ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA (2011, background): “Polynomials orthogonal to a truncated Gaussian measure are referred to as Rys polynomials [20].”
Orthogonal polynomials (2005, unknown): “Nonetheless, for the case r = 1, and µ0, µ1 ∈ Reg (see Section 9) it was shown in Gautschi–Kuijlaars [29] that the asymptotic distribution of the zeros of the derivative Q′n is the equilibrium measure ωE0∪E1 , where Ei is the support of µi, i = 0, 1 (which also have to be assumed to be regular).”