scholarly journals Orthogonal polynomials and Gaussian quadrature for refinable weight functions

2004 ◽  
Vol 17 (3) ◽  
pp. 241-258 ◽  
Author(s):  
D.P. Laurie ◽  
J.M. de Villiers
Keyword(s):  
Orthogonal Polynomials ◽  
Gaussian Quadrature ◽  
Weight Functions

A New Composite Quadrature Rule

2013 ◽  
Vol 5 (04) ◽  
pp. 595-606
Author(s):  
Weiwei Sun ◽  
Qian Zhang
Keyword(s):  
Boundary Conditions ◽  
Orthogonal Polynomials ◽  
Quadrature Rule ◽  
Numerical Results ◽  
Weight Functions

AbstractWe present a new composite quadrature rule which is exact for polynomials of degree 2N+K– 1 withNabscissas at each subinterval andKboundary conditions. The corresponding orthogonal polynomials are introduced and the analytic formulae for abscissas and weight functions are presented. Numerical results show that the new quadrature rule is more efficient, compared with classical ones.

Padé approximation and orthogonal polynomials

1974 ◽  
Vol 10 (2) ◽  
pp. 263-270 ◽  
Author(s):  
G.D. Allen ◽  
C.K. Chui ◽  
W.R. Madych ◽  
F.J. Narcowich ◽  
P.W. Smith
Keyword(s):  
Power Series ◽  
Variational Method ◽  
Orthogonal Polynomials ◽  
Gaussian Quadrature ◽  
Quadrature Formulas ◽  
The Past ◽  
Gaussian Quadrature Formulas ◽  
Poles And Zeros ◽  
Formal Power ◽  
Determinant Theory

By using a variational method, we study the structure of the Padé table for a formal power series. For series of Stieltjes, this method is employed to study the relations of the Padé approximants with orthogonal polynomials and gaussian quadrature formulas. Hence, we can study convergence, precise locations of poles and zeros, monotonicity, and so on, of these approximants. Our methods have nothing to do with determinant theory and the theory of continued fractions which were used extensively in the past.

Complex Weight Functions for Classical Orthogonal Polynomials

1991 ◽  
Vol 43 (6) ◽  
pp. 1294-1308 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
David R. Masson ◽  
Mizan Rahman
Keyword(s):  
Orthogonal Polynomials ◽  
Weight Functions ◽  
Classical Orthogonal Polynomials ◽  
The Real ◽  
Complex Functions ◽  
Wilson Polynomials ◽  
Distributional Weight

AbstractWe give complex weight functions with respect to which the Jacobi, Laguerre, little q-Jacobi and Askey-Wilson polynomials are orthogonal. The complex functions obtained are weight functions in a wider range of parameters than the real weight functions. They also provide an alternative to the recent distributional weight functions of Morton and Krall, and the more recent hyperfunction weight functions of Kim.

Maximum of the modulus of kernels of Gaussian quadrature formulae for one class of Bernstein–Szegő weight functions

2012 ◽  
Vol 218 (9) ◽  
pp. 5746-5756 ◽  
Author(s):  
Miodrag M. Spalević ◽  
Miroslav S. Pranić ◽  
Aleksandar V. Pejčev
Keyword(s):  
Gaussian Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae

Polynomial inequalities in regions with corners in theweighted Lebesgue spaces

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5647-5670 ◽  
Author(s):  
Fahreddin Abdullayev
Keyword(s):  
Orthogonal Polynomials ◽  
Lebesgue Space ◽  
Weight Functions ◽  
Weighted Lebesgue Space ◽  
Algebraic Polynomials ◽  
Lebesgue Spaces ◽  
Polynomial Inequalities

In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in regions with corners in a weighted Lebesgue space, where the singularities of contour and the weight functions satisfy some condition.

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