CONVERGENCE OF PRODUCT INTEGRATION RULES FOR WEIGHTS ON THE WHOLE REAL LINE

1993 ◽  
pp. 255-270
Author(s):  
D. S. LUBINSKY
Keyword(s):  
Real Line ◽  
Product Integration ◽  
Integration Rules

Hermite and Hermite-Fejer Interpolation and Associated Product Integration Rules on the Real Line: The L1 Theory

1992 ◽  
Vol 44 (3) ◽  
pp. 561-590 ◽  
Author(s):  
D. S. Lubinsky ◽  
P. Rabinowitz
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Rapid Growth ◽  
Hermite Interpolation ◽  
Point Of View ◽  
Product Integration ◽  
The Real ◽  
Highly Oscillatory ◽  
New Feature ◽  
Integration Rules

AbstractWe investigate convergence in a weighted L1 -norm of Hermite-Fejér and Hermite interpolation at the zeros of orthogonal polynomials associated with weights on the real line. The results are then applied to convergences of product integration rules. From the point of view of orthogonal polynomials, the new feature is that Freud and Erdös weights are treated simultaneously and that relatively few assumptions are placed on the weight. From the point of view of product integration, the rules exhibit convergence for highly oscillatory kernels (for example) and for functions of rapid growth at infinity.

scholarly journals Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 102093-102105 ◽  
Author(s):  
Amr M. Abdelaty ◽  
Merna Roshdy ◽  
Lobna A. Said ◽  
Ahmed G. Radwan
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Product Integration ◽  
Integration Rules

scholarly journals Interpolatory product integration for Riemann-integrable functions

1987 ◽  
Vol 29 (2) ◽  
pp. 195-202 ◽  
Author(s):  
Philip Rabinowitz ◽  
William E. Smith
Keyword(s):  
Orthogonal Polynomials ◽  
Integration Interval ◽  
Product Integration ◽  
Zeros Of Orthogonal Polynomials ◽  
Integrable Functions ◽  
Riemann Integrable Functions ◽  
Integration Rules

AbstractConditions are fround for the convergence of intepolatory product integration rules and the corresponding companion rules for the class of Riemann-integrable functions. These condtions are used to prove convergence for several classes of rules based on sets of zeros of orthogonal polynomials possibly augmented by one both of the endpoints of the integration interval.

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