Results 141 to 150 of about 139,435 (183)
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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 ...
Wilhelm Magnus +2 more
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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 ...
Wilhelm Magnus +2 more
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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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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 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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Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2011Satoru Odake
exaly
On Generating Orthogonal Polynomials
SIAM Journal on Scientific and Statistical Computing, 1982Walter Gautschi
exaly
An extended class of orthogonal polynomials defined by a Sturm–Liouville problem
Journal of Mathematical Analysis and Applications, 2009David Gomez-Ullate, Robert Milson
exaly