Abstract
Given a linear operator equation Kf=g with data g(x i )i=1,…,n, we consider the general moment collocation solution defined as the function f n that minimizes ||Pf n ||2 over a Hilbert space, subject to Kf n (x i )=g(x i )i=1,…,n. Here P is an orthogonal projection with a finite dimensional null space. In the case of P=I, the identity, it is known that if a certain kernel depending on K is continuous, then f n → f 0 , the true solution, as the maximum subinterval width → 0. Moreover, if the kernel satisfies a smoothness condition, then rates of convergence are known. In this paper we extend these results to the case with general P.
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.