Results 321 to 330 of about 996,598 (373)
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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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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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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 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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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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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
Berti, A. C. +2 more
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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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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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2004
This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration.
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This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration.
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