Results 281 to 290 of about 15,437 (317)
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Numerical Algorithms, 1996
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Syvert P. Nørsett, Bente Østigård
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Syvert P. Nørsett, Bente Østigård
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Constructing Orthogonal Polynomials
Missouri Journal of Mathematical Sciences, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1966
Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Orthogonal Polynomial Regression
International Statistical Review / Revue Internationale de Statistique, 1979Summary We discuss in basic terms the orthogonal polynomial regression approach for curve fitting when the independent variable occurs at unequal intervals and is observed with unequal frequency. The computations required for determining orthogonal polynomials are described with a simple example.
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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 utilizes the main mirror composed of thirty-six hexagonal segments. By use of the representation theory of the symmetry group of the hexagon a
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SIAM Journal on Numerical Analysis, 1981
We give the relation between Hermite–Pade 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–Pade 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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Galerkin orthogonal polynomials
Journal of Computational Physics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Multivariate Orthogonal Polynomials
SIAM Journal on Mathematical Analysis, 1993Summary: Orthogonal polynomials in several variables are studied. The results include a new formulation of the recurrence relation, characterization of orthogonality of polynomial sequences, an analogy of Christoffel-Darboux formula, and properties of reproducing kernel function.
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