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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On constructing least squares solutions to two-point boundary value problems

Author: John Locker
Journal: Trans. Amer. Math. Soc. 203 (1975), 175-183
MSC: Primary 34B05; Secondary 65L10
MathSciNet review: 0372303
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Abstract: For an $ n$th order linear boundary value problem $ Lf = {g_0}$ in the Hilbert space $ {L^2}[a,b]$, a sequence of approximate solutions is constructed which converges to the unique least squares solution of minimal norm. The method is practical from a computational viewpoint, and it does not require knowing the null spaces of the differential operator $ L$ or its adjoint $ {L^ \ast }$.

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Keywords: Least squares solution, boundary value problem, approximation scheme, generalized inverse
Article copyright: © Copyright 1975 American Mathematical Society