Symbolic–numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal B-spline

The first 60 coefficients in the three-term recurrence relation for monic polynomials orthogonal with respect to cardinal B -splines φ m as the weight functions on [0, m ] ( m ∈ ℕ) are obtained in a symbolic form. They enable calculation of parameters, nodes, and weights, in the corresponding Gaussi...

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Bibliographic Details
Published in:Numerical algorithms Vol. 76; no. 2; pp. 333 - 347
Main Author: Milovanović, Gradimir V.
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2017
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
B spline functions
Computer Science
Eigenvalues
Nodes
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Quadratures
Theory of Computation
Weighting functions
41A55
65D30
Moment
Recurrence relation
Gaussian quadrature formula
Cardinal
65D32
spline
Symbolic computation
41A15
Orthogonal polynomial
42C05
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The first 60 coefficients in the three-term recurrence relation for monic polynomials orthogonal with respect to cardinal B -splines φ m as the weight functions on [0, m ] ( m ∈ ℕ) are obtained in a symbolic form. They enable calculation of parameters, nodes, and weights, in the corresponding Gaussian quadrature up to 60 nodes. The efficiency of these Gaussian quadratures is shown in some numerical examples. Finally, two interesting conjectures are stated.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-016-0256-y