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

Locker, John

doi:10.1090/S0002-9947-1975-0372303-0

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

Trans. Amer. Math. Soc. 203 (1975), 175-183

DOI: https://doi.org/10.1090/S0002-9947-1975-0372303-0

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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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