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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuous dependence of least squares solutions of linear boundary value problems


Authors: R. Kannan and John Locker
Journal: Proc. Amer. Math. Soc. 59 (1976), 107-110
MSC: Primary 34B05
MathSciNet review: 0409947
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Abstract: Let $ {u_\lambda }$ be the unique least squares solution of minimal norm of the linear boundary value problem $ Lu - \lambda u = f$, where $ L$ is a selfadjoint differential operator in $ {L^2}[a,b]$. Working in the Sobolev space $ {H^n}[a,b]$, the alternative method is used to examine the continuous dependence of the $ {u_\lambda }$ on the parameter $ \lambda $ as $ \lambda \to {\lambda _0}$, and the convergent and divergent cases are both characterized.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0409947-X
PII: S 0002-9939(1976)0409947-X
Keywords: Continuous dependence, least squares solution, boundary value problem, generalized inverse, alternative method
Article copyright: © Copyright 1976 American Mathematical Society