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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] L. Cesari, Nonlinear analysis, Lecture Notes, C. I. M. E., Bressanone, 1972. MR 0407672 (53:11444)
  • [2] J. K. Hale, Applications of alternative problems, Lecture Notes, Brown University, Providence, Rhode Island, 1971.
  • [3] J. Locker, On constructing least squares solutions to two-point boundary value problems, Trans. Amer. Math. Soc. 203 (1975), 175-183. MR 0372303 (51:8519)

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Keywords: Continuous dependence, least squares solution, boundary value problem, generalized inverse, alternative method
Article copyright: © Copyright 1976 American Mathematical Society

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