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Orthogonal Polynomial Wavelets
Numerical Algorithms, 2002The authors construct orthogonal polynomial wavelets and extend some results of \textit{B. Fischer} and \textit{J. Prestin} [Math. Comput. 66, No. 220, 1593-1618 (1997; Zbl 0896.42020)]. Let \(P_j\) \((j= 0,1,\dots)\) be orthonormal polynomials on \([a,b]\) \((-\infty\leq a< b\leq\infty)\) with respect to a nonnegative weight function \(w\).
Fischer B, Themistoclakis W
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Orthogonal Polynomials Associated with Related Measures and Sobolev Orthogonal Polynomials
Numerical Algorithms, 2003Let \(d\mu_1\) and \(d\mu_2\) be two measures with the same support \(E\). They are said to be related to each other by a first degree polynomial multiplication, if \[ (x-q)d\mu_1(x)=cd\mu_2(x), \] where the first degree polynomial \(c^{-1}(x-q)\) is positive on \(E\). The authors study the connection between two sequences of orthogonal polynomials and
A. C. Berti +2 more
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Computing orthogonal polynomials
Computers & Operations Research, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Frank G. Landram, Bahram Alidaee
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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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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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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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On Multivariate Orthogonal Polynomials
SIAM Journal on Mathematical Analysis, 1993Orthogonal polynomials in several variables are studied. The results include a newformulation 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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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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ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS
International Journal of Numerical Analysis and Modeling, 2018In this survey article, we present some recent results on the asymptotic behavior of four systems of orthogonal polynomials. These are Stieltjes-Wigert, Hahn, Racah and pseudo-Jacobi polynomials. In each case, the variable $z$ is allowed to be in any part of the complex plane. In some cases, asymptotic formulas are also given for their zeros.
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