Abstract
The question of the convergence of a sequence of product-type quadrature formulas to the integral as the number of nodes becomes unbounded is examined. Conditions on the functions in the integrand and the weights and nodes in the quadrature formulas are stated which insure the convergence of the quadrature process. For example, it is shown that if the functions in the integrand are holomorphic in certain regions of the complex plane which depend upon the nodes used in the quadrature process, then the product-type interpolatory quadrature process converges. Also, necessary and sufficient conditions are given for the convergence of the general product-type quadrature process whenever the functions in the integrand are continuous.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.