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Orthogonal Polynomials on the Hexagon
SIAM Journal on Applied Mathematics, 1987Least-square approximation by polynomials, with respect to area measure on the regular hexagon, is useful in the construction and analysis of hexagonal optical elements. Notably the Keck Ten-Meter Telescope will utilize a main mirror composed of thirty-six hexagonal segments.
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SIAM Journal on Numerical Analysis, 1981
We give the relation between Hermite–Padé approximants and vector orthogonal polynomials. An algorithm for calculating vector orthogonal polynomials near the diagonal is described. An exact multiple integral formula for vector orthogonal polynomials is proved.
Burley, S. K., John, S. O., Nuttall, J.
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We give the relation between Hermite–Padé approximants and vector orthogonal polynomials. An algorithm for calculating vector orthogonal polynomials near the diagonal is described. An exact multiple integral formula for vector orthogonal polynomials is proved.
Burley, S. K., John, S. O., Nuttall, J.
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On expansions in orthogonal polynomials
Advances in Computational Mathematics, 2011In 2011, \textit{A. Iserles} [Numer. Math. 117, No. 3, 529--553 (2011; Zbl 1211.33001)] introduced an \(\mathcal{O}(N \log N)\) algorithm for the computation of the first \(N\) coefficients in an expansion of an analytic function in Legendre polynomials.
María José Cantero, Arieh Iserles
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Siberian Mathematical Journal, 2001
The author presents an extension of a system of orthogonal polynomials on a finite set by using a transformation of weights of orthogonality. It is shown that if certain weights of orthogonality are negative, then the roots of the system of polynomials (under a specific selection of weights) are real and, moreover, these roots are weakly separated. The
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The author presents an extension of a system of orthogonal polynomials on a finite set by using a transformation of weights of orthogonality. It is shown that if certain weights of orthogonality are negative, then the roots of the system of polynomials (under a specific selection of weights) are real and, moreover, these roots are weakly separated. The
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On Generating Orthogonal Polynomials
SIAM Journal on Scientific and Statistical Computing, 1982We consider the problem of numerically generating the recursion coefficients of orthogonal polynomials, given an arbitrary weight distribution of either discrete, continuous, or mixed type. We discuss two classical methods, respectively due to Stieltjes and Chebyshev, and modern implementations of them, placing particular emphasis on their numerical ...
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Galerkin orthogonal polynomials
Journal of Computational Physics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Orthogonal polynomials—centroid of their zeroes
Numerical Algorithms, 2008Given and orthogonal polynomial sequence \((P_n)_n\), the centroid of the zeros of the \(n\)-th polynomial \(P_n\) is defined by \(s_n=\frac1n\sum_{k=1}^n x_{n,k}\), where \(x_{n,k}\), \(k=1,2,\dots,n\) are the roots of \(P_n\). In the present paper the author reviews some properties of the zeros and the centroid (such as inequalities, invariance with ...
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Binomial-Weighted Orthogonal Polynomials
Journal of the ACM, 1967This paper discusses a set of polynomials, {φ r ( s )}, orthogonal over a discrete range, with binomial distribution, b ( s ; n , p ), as the weighting function.
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On an estimate for orthogonal polynomials
1989See the review in Zbl 0603.42021.
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